McKean, Henry P. (Henry Pratt) 1930
Overview
Works:  46 works in 181 publications in 4 languages and 3,723 library holdings 

Genres:  Conference papers and proceedings Academic theses 
Roles:  Author, Editor, Honoree, Contributor, Dedicatee 
Classifications:  QA273, 515.2433 
Publication Timeline
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Most widely held works about
Henry P McKean
 Henry Pratt McKean by Zeta Psi Fraternity( )
 Mckean, Henry P. : mathematics( )
Most widely held works by
Henry P McKean
Fourier series and integrals by
H Dym(
Book
)
26 editions published between 1972 and 2003 in English and held by 768 WorldCat member libraries worldwide
26 editions published between 1972 and 2003 in English and held by 768 WorldCat member libraries worldwide
Stochastic integrals by
Henry P McKean(
Book
)
33 editions published between 1969 and 2005 in 3 languages and held by 688 WorldCat member libraries worldwide
33 editions published between 1969 and 2005 in 3 languages and held by 688 WorldCat member libraries worldwide
Diffusion processes and their sample paths by
Kiyosi Itō(
Book
)
24 editions published between 1965 and 1996 in 3 languages and held by 575 WorldCat member libraries worldwide
U4 = Reihentext + Werbetext für dieses Buch Werbetext: Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one or more dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean
24 editions published between 1965 and 1996 in 3 languages and held by 575 WorldCat member libraries worldwide
U4 = Reihentext + Werbetext für dieses Buch Werbetext: Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one or more dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean
Gaussian processes, function theory, and the inverse spectral problem by
H Dym(
Book
)
12 editions published between 1976 and 2008 in English and held by 462 WorldCat member libraries worldwide
12 editions published between 1976 and 2008 in English and held by 462 WorldCat member libraries worldwide
Elliptic curves : function theory, geometry, arithmetic by
Henry P McKean(
Book
)
12 editions published between 1997 and 2012 in English and held by 409 WorldCat member libraries worldwide
The subject of elliptic curves is one of the jewels of nineteenthcentury mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. The treatment combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetics. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics. The many exercises with hints scattered throughout the text give the reader a glimpse of further developments
12 editions published between 1997 and 2012 in English and held by 409 WorldCat member libraries worldwide
The subject of elliptic curves is one of the jewels of nineteenthcentury mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. The treatment combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetics. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics. The many exercises with hints scattered throughout the text give the reader a glimpse of further developments
Stochastic differential equations by
Mark Kac(
Book
)
12 editions published between 1967 and 1973 in English and held by 339 WorldCat member libraries worldwide
12 editions published between 1967 and 1973 in English and held by 339 WorldCat member libraries worldwide
Probability, geometry, and integrable systems : for Henry McKean's seventyfifth birthday by
Mark A Pinsky(
Book
)
9 editions published between 2008 and 2011 in English and held by 184 WorldCat member libraries worldwide
9 editions published between 2008 and 2011 in English and held by 184 WorldCat member libraries worldwide
Probability : the classical limit theorems by
Henry P McKean(
Book
)
13 editions published in 2014 in English and held by 115 WorldCat member libraries worldwide
The theory of probability has been extraordinarily successful at describing a variety of natural phenomena, from the behavior of gases to the transmission of information, and is a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bellshaped curve, the law of averages, and so on, concepts that crop up in so many settings that they are, in some sense, universal. This universality is predicted by probability theory to a remarkable degree. It is the aim of the book to explain the theory, prove classical limit theorems, and investigate their ramifications. The author assumes a good working knowledge of basic analysis, real and complex. From this, he maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text
13 editions published in 2014 in English and held by 115 WorldCat member libraries worldwide
The theory of probability has been extraordinarily successful at describing a variety of natural phenomena, from the behavior of gases to the transmission of information, and is a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bellshaped curve, the law of averages, and so on, concepts that crop up in so many settings that they are, in some sense, universal. This universality is predicted by probability theory to a remarkable degree. It is the aim of the book to explain the theory, prove classical limit theorems, and investigate their ramifications. The author assumes a good working knowledge of basic analysis, real and complex. From this, he maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text
Universal symplectic forms in the soliton theory by Fedor Soloviev(
)
1 edition published in 2010 in English and held by 9 WorldCat member libraries worldwide
Using KricheverPhong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multipole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a byproduct, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. KricheverPhong's formula provides a hierarchy of symplectic structures, and we show that there exists a nontrivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points
1 edition published in 2010 in English and held by 9 WorldCat member libraries worldwide
Using KricheverPhong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multipole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a byproduct, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. KricheverPhong's formula provides a hierarchy of symplectic structures, and we show that there exists a nontrivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points
The nonlinear Schroedinger equation with a delta potential and even initial data by Jungwoon Park(
)
1 edition published in 2010 in English and held by 9 WorldCat member libraries worldwide
We consider the onedimensional focusing nonlinear Schrodinger equation (NLS) on R with a delta potential qdelta0(x) and even initial data. Due to the specific choice of the potential and initial data, the equation reduces to the initial boundary value (IBV) problem for the NLS equation on a halfline with homogeneous boundary conditions at x = 0: such problems are known to be integrable by an extension of the inverse scattering method
1 edition published in 2010 in English and held by 9 WorldCat member libraries worldwide
We consider the onedimensional focusing nonlinear Schrodinger equation (NLS) on R with a delta potential qdelta0(x) and even initial data. Due to the specific choice of the potential and initial data, the equation reduces to the initial boundary value (IBV) problem for the NLS equation on a halfline with homogeneous boundary conditions at x = 0: such problems are known to be integrable by an extension of the inverse scattering method
A Baernstein problem of pharmonic measures and an invariance of pharmonic functions under boundary perturbations using tugofwar
with noise by Sungwook Kim(
)
1 edition published in 2010 in English and held by 8 WorldCat member libraries worldwide
Given a planar domain O and p & isin; (1, infinity), let Hf denote the pharmonic extension to O of a boundary function f : & part;O & rarr; R (as defined via Perron's method). We show that if f is a piecewise continuous function, O is piecewise smooth near where f is discontinuous, and g is a bounded function on & part;O such that g = f on & part;O\ E where E & sub; R2 is a countable set with op(E, O) = 0, then Hf = H g. In particular, this solves a problem posed by Baernstein in 1998, who asked the question for 01 valued F and F & tilde; on the unit circle; it extends work of Bjorn, Bjorn, and Shanmugalingam, who answered the question for 1 <p & le; 2. A key step is to show that pharmonic extensions approximately agree with harmonic extensions in a neighborhood of a jump discontinuity
1 edition published in 2010 in English and held by 8 WorldCat member libraries worldwide
Given a planar domain O and p & isin; (1, infinity), let Hf denote the pharmonic extension to O of a boundary function f : & part;O & rarr; R (as defined via Perron's method). We show that if f is a piecewise continuous function, O is piecewise smooth near where f is discontinuous, and g is a bounded function on & part;O such that g = f on & part;O\ E where E & sub; R2 is a countable set with op(E, O) = 0, then Hf = H g. In particular, this solves a problem posed by Baernstein in 1998, who asked the question for 01 valued F and F & tilde; on the unit circle; it extends work of Bjorn, Bjorn, and Shanmugalingam, who answered the question for 1 <p & le; 2. A key step is to show that pharmonic extensions approximately agree with harmonic extensions in a neighborhood of a jump discontinuity
Gaussian processes, and the inverse spectral problem by
H Dym(
Book
)
1 edition published in 1976 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1976 in English and held by 8 WorldCat member libraries worldwide
Difusion processes and their sample paths by
Kiyosi Itō(
)
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
Harmonic functions for random walks in random environments by Paris Pender(
Book
)
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
We consider random walks in stationary ergodic random environments. In the case of uniformly elliptic walks, we prove the existence of quenched harmonic functions of the form etheta·x+f (x) for some sublinear f, and a specific class of theta. We then move to a spacetime environment and prove minimality theorems for such functions in a special case
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
We consider random walks in stationary ergodic random environments. In the case of uniformly elliptic walks, we prove the existence of quenched harmonic functions of the form etheta·x+f (x) for some sublinear f, and a specific class of theta. We then move to a spacetime environment and prove minimality theorems for such functions in a special case
Randomly trapped random walks by Roman Royfman(
Book
)
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
The model introduced in this work model, Randomly Trapped Random Walk (RTRW), is a general framework to study a onedimensional motion in a random trapping environment. We develop tools to study its scaling limits. We discover that all possible limits of RTRW can be represented as a Brownian motion timechanged by a Levy subordinator. More precisely, we will show that if the trapping landscape is homogeneous, RTRW exhibits diffusive behavior. On the other hand, in inhomogeneous environments, RTRW is nondiffusive. The set of possible limits of RTRW (in inhomogeneous environments) is extremely rich. In particular, it includes Fractional Kinetics, which was initially introduced as a scaling limit of Continuous Time Random Walk, as well as a new broad class of processes, which we call Randomly Trapped Brownian Motions. This class contains a singular diffusion, which was recently introduced by Fontes, Isopi and Newman. We give various examples, some of the of a geometric nature, i.e. the Comb Model
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
The model introduced in this work model, Randomly Trapped Random Walk (RTRW), is a general framework to study a onedimensional motion in a random trapping environment. We develop tools to study its scaling limits. We discover that all possible limits of RTRW can be represented as a Brownian motion timechanged by a Levy subordinator. More precisely, we will show that if the trapping landscape is homogeneous, RTRW exhibits diffusive behavior. On the other hand, in inhomogeneous environments, RTRW is nondiffusive. The set of possible limits of RTRW (in inhomogeneous environments) is extremely rich. In particular, it includes Fractional Kinetics, which was initially introduced as a scaling limit of Continuous Time Random Walk, as well as a new broad class of processes, which we call Randomly Trapped Brownian Motions. This class contains a singular diffusion, which was recently introduced by Fontes, Isopi and Newman. We give various examples, some of the of a geometric nature, i.e. the Comb Model
Marking the (1,2) points of the Brownian web and applications by
Emmanuel Schertzer(
Book
)
1 edition published in 2007 in English and held by 2 WorldCat member libraries worldwide
Another topic treated in this thesis concerns some fine properties of the "dynamical random walk" starting from the origin in the DyDW. In particular, we prove the existence of a set of dynamical times of Hausdorff dimension one at which the dynamical random walk violates the law of the iterated logarithm (LIL)
1 edition published in 2007 in English and held by 2 WorldCat member libraries worldwide
Another topic treated in this thesis concerns some fine properties of the "dynamical random walk" starting from the origin in the DyDW. In particular, we prove the existence of a set of dynamical times of Hausdorff dimension one at which the dynamical random walk violates the law of the iterated logarithm (LIL)
Advances in mathematics(
Book
)
in Undetermined and English and held by 2 WorldCat member libraries worldwide
in Undetermined and English and held by 2 WorldCat member libraries worldwide
Large deviation lower bounds for the totally asymmetric simple exclusion process by Yevgeny Vilensky(
Book
)
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
The totally asymmetric simple exclusion process (TASEP) has been shown to have a hydrodynamic scaling limit under the hyperbolic scaling of space and time. This limit is a measure, whose density with respect to Lebesgue measure is given by the unique entropy weak solution to a nonlinear partial differential equation in conservation form. Large deviations for this problem had been studied by Jensen in his thesis, who proved the upper bound and obtained a lower bound result for nonentropic weak solutions that are constant away from a single line of constant speed [3]. The subject of this thesis is the extension of the lower bound result to a wider class of nonentropic weak solutions. In particular, we show that for weak solutions that are entropic away from smooth curves and which have sufficient regularity, the lower bound holds. We prove locality results that show that the entropy of a modified TASEP (relative to a standard TASEP), with modifications applied locally at macroscopically separated sites, can be decomposed into the sum, over all such sites, of the relative entropies of TASEPs with just one modification
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
The totally asymmetric simple exclusion process (TASEP) has been shown to have a hydrodynamic scaling limit under the hyperbolic scaling of space and time. This limit is a measure, whose density with respect to Lebesgue measure is given by the unique entropy weak solution to a nonlinear partial differential equation in conservation form. Large deviations for this problem had been studied by Jensen in his thesis, who proved the upper bound and obtained a lower bound result for nonentropic weak solutions that are constant away from a single line of constant speed [3]. The subject of this thesis is the extension of the lower bound result to a wider class of nonentropic weak solutions. In particular, we show that for weak solutions that are entropic away from smooth curves and which have sufficient regularity, the lower bound holds. We prove locality results that show that the entropy of a modified TASEP (relative to a standard TASEP), with modifications applied locally at macroscopically separated sites, can be decomposed into the sum, over all such sites, of the relative entropies of TASEPs with just one modification
Universality of random Hamiltonians by Alexey Kuptsov(
Book
)
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
We introduce a new REM universality conjecture for levels of random Hamiltonians, in the same spirit as the local REM conjecture made by S. Mertens and H. Bauke. We establish our conjecture for a wide class of Gaussian and nonGaussian Hamiltonians, which include the pspin models, the SherringtonKirkpatrick model and the number partitioning problem. We prove that our universality result is optimal for the last two models by showing when this universality breaks down. In addition, we improve the previously known results on Merten's conjecture. In particular, we prove that the local REM universality holds for pspin models with p larger than 2 for energy scales of the same order as the maximum
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
We introduce a new REM universality conjecture for levels of random Hamiltonians, in the same spirit as the local REM conjecture made by S. Mertens and H. Bauke. We establish our conjecture for a wide class of Gaussian and nonGaussian Hamiltonians, which include the pspin models, the SherringtonKirkpatrick model and the number partitioning problem. We prove that our universality result is optimal for the last two models by showing when this universality breaks down. In addition, we improve the previously known results on Merten's conjecture. In particular, we prove that the local REM universality holds for pspin models with p larger than 2 for energy scales of the same order as the maximum
My methods in breeding poultry by
Henry P McKean(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
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Related Identities
 Dym, H. (Harry) 1938 Author
 Itō, Kiyosi 19152008 Author
 Moll, Victor H. 1956
 Keller, Joseph B. (Joseph Bishop) 19232016 Editor
 American Mathematical Society Other Publisher Editor
 Society for Industrial and Applied Mathematics Other Publisher Editor
 Pinsky, Mark A. 1940 Editor
 Birnir, Björn Editor
 Ben Arous, Gerard
 Sheffield, Scott
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Associated Subjects
Brownian motion processes Brownian movements Canada Curves, Elliptic Diffusion Diffusion processes Distribution (Probability theory) Fourier series Gaussian processes Geometry, Algebraic Geometry, Differential Hamiltonian systems Hardy spaces Limit theorems (Probability theory) Mathematics Potential theory (Mathematics) PoultryBreeding Prediction theory Probabilities Scientists Spectral theory (Mathematics) Stationary processes Stochastic differential equations Stochastic integrals Stochastic processes United States
Alternative Names
Henry McKean American mathematician at New York University
Henry McKean Amerikaans wiskundige
Henry McKean amerikansk matematikar
Henry McKean amerikansk matematiker
Henry McKean mathématicien américain
Henry McKean USamerikanischer Mathematiker
Mac Kean, Henry P.
Mac Kean Henry P. 1930....
Mac Kean, Henry Pratt 1930
MacKean, Henry P.
MacKean Henry P. 1930....
MacKean, Henry Pratt 1930
Makkin, G.
Makkin, G. 1930
Mc Kean, Henry P.
Mc Kean Henry P. 1930....
Mc Kean, Henry Pratt 1930
McKean, H. P.
McKean, H. P. 1930
McKean, H. P. 1930 Jr
McKean, H. P. (Henry P.)
McKean, H. P. (Henry P.), 1930
McKean, H. P. (Henry P.), Jr., 1930
McKean, H. P. Jr
McKean, Henry.
McKean, Henry 1930
McKean, Henry P.
McKean, Henry P. 1930 Jr
McKean, Henry P. Jr
McKean, Henry P. Jr. 1930
McKean, Henry Pratt 1930
Маккин, Г
Маккин, Г. (Генри П.)
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