Grimmett, Geoffrey
Overview
Works:  37 works in 347 publications in 3 languages and 5,399 library holdings 

Genres:  Conference proceedings Textbooks 
Roles:  Author, Editor, Creator 
Classifications:  QA273, 519.2 
Publication Timeline
.
Most widely held works by
Geoffrey Grimmett
Probability and random processes by
Geoffrey Grimmett(
Book
)
117 editions published between 1982 and 2009 in English and held by 1,544 WorldCat member libraries worldwide
This textbook provides a wideranging and entertaining indroduction to probability and random processes and many of their practical applications. It includes many exercises and problems with solutions
117 editions published between 1982 and 2009 in English and held by 1,544 WorldCat member libraries worldwide
This textbook provides a wideranging and entertaining indroduction to probability and random processes and many of their practical applications. It includes many exercises and problems with solutions
Percolation by
Geoffrey Grimmett(
Book
)
25 editions published between 1989 and 2011 in English and Undetermined and held by 788 WorldCat member libraries worldwide
The mathematical theory of percolation has acquired something of a reputation for inaccessibility. In addition, several recent advances of substance have tossed the historical order of discovery on its head. It is time to reexamine the subject afresh, in light of recent discoveries. This book does just that. It contains a definitive and coherent account of the subject, in an orderly way accessible to the nonspecialist, including the shortest and neatest proofs currently known. In order to maximize accessibility, it concentrates on bond percolation on the ddimensional cubic lattice where d>2. The subcritical and supercritical phases are described in considerable detail; the recent proofs of the uniqueness of critical points and the infinite open cluster are used extensively. There are two chapters devoted to a lucid account of the physical theory of scaling the renormalization in the context of percolation. There is a chapter dealing with the case of two dimensions, including a rather short proof of the famous exact calculation of + for the critical probability. The book terminates with a collection of pencil sketches of related areas of mathematics and physics
25 editions published between 1989 and 2011 in English and Undetermined and held by 788 WorldCat member libraries worldwide
The mathematical theory of percolation has acquired something of a reputation for inaccessibility. In addition, several recent advances of substance have tossed the historical order of discovery on its head. It is time to reexamine the subject afresh, in light of recent discoveries. This book does just that. It contains a definitive and coherent account of the subject, in an orderly way accessible to the nonspecialist, including the shortest and neatest proofs currently known. In order to maximize accessibility, it concentrates on bond percolation on the ddimensional cubic lattice where d>2. The subcritical and supercritical phases are described in considerable detail; the recent proofs of the uniqueness of critical points and the infinite open cluster are used extensively. There are two chapters devoted to a lucid account of the physical theory of scaling the renormalization in the context of percolation. There is a chapter dealing with the case of two dimensions, including a rather short proof of the famous exact calculation of + for the critical probability. The book terminates with a collection of pencil sketches of related areas of mathematics and physics
The randomcluster model by
Geoffrey Grimmett(
)
26 editions published between 2006 and 2009 in English and German and held by 652 WorldCat member libraries worldwide
"The randomcluster model has emerged in recent years as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. This systematic study includes accounts of the subcritical and supercritical phases, together with clear statements of important open problems. There is an extensive treatment of the firstorder (discontinuous) phase transition, as well as a chapter devoted to applications of the randomcluster method to other models of statistical physics."Résumé de l'éditeur
26 editions published between 2006 and 2009 in English and German and held by 652 WorldCat member libraries worldwide
"The randomcluster model has emerged in recent years as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. This systematic study includes accounts of the subcritical and supercritical phases, together with clear statements of important open problems. There is an extensive treatment of the firstorder (discontinuous) phase transition, as well as a chapter devoted to applications of the randomcluster method to other models of statistical physics."Résumé de l'éditeur
Probability : an introduction by
Geoffrey Grimmett(
Book
)
31 editions published between 1986 and 2014 in English and Undetermined and held by 482 WorldCat member libraries worldwide
31 editions published between 1986 and 2014 in English and Undetermined and held by 482 WorldCat member libraries worldwide
One thousand exercises in probability by
Geoffrey Grimmett(
Book
)
29 editions published between 2001 and 2011 in English and Undetermined and held by 390 WorldCat member libraries worldwide
This is an updated and greatly expanded version of an already wellestablished and popular exercise manual. It provides a wideranging selection of illuminating, informative and entertaining problems, together with their solution.Topics include modelling and many applications of probability theory, as well as theoretical aspects. There are questions at all ability levels, the majority being of elementary or intermediate standard.Well suited as a stand alone problems and solutions manual, it also is the companion volume for
29 editions published between 2001 and 2011 in English and Undetermined and held by 390 WorldCat member libraries worldwide
This is an updated and greatly expanded version of an already wellestablished and popular exercise manual. It provides a wideranging selection of illuminating, informative and entertaining problems, together with their solution.Topics include modelling and many applications of probability theory, as well as theoretical aspects. There are questions at all ability levels, the majority being of elementary or intermediate standard.Well suited as a stand alone problems and solutions manual, it also is the companion volume for
Probability on graphs : random processes on graphs and lattices by
Geoffrey Grimmett(
Book
)
17 editions published between 2010 and 2013 in English and held by 373 WorldCat member libraries worldwide
Inspiration and provocation from a master expositor, taking you to the heart of contemporary probability
17 editions published between 2010 and 2013 in English and held by 373 WorldCat member libraries worldwide
Inspiration and provocation from a master expositor, taking you to the heart of contemporary probability
Lecture on probability theory and statistics : Ecole d'eté de probabilités de SaintFlour XXVI  1996 by
Evarist Giné(
Book
)
15 editions published between 1996 and 1997 in English and German and held by 336 WorldCat member libraries worldwide
Nur Contents aufnehmen
15 editions published between 1996 and 1997 in English and German and held by 336 WorldCat member libraries worldwide
Nur Contents aufnehmen
Disorder in physical systems : a volume in honour of John M. Hammersley on the occasion of his 70th birthday(
Book
)
9 editions published in 1990 in English and held by 237 WorldCat member libraries worldwide
9 editions published in 1990 in English and held by 237 WorldCat member libraries worldwide
Combinatorics, complexity, and chance : a tribute to Dominic Welsh by
Geoffrey Grimmett(
Book
)
17 editions published between 2007 and 2009 in English and held by 220 WorldCat member libraries worldwide
Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. This volume summarises and reviews the consistent themes from his work through a series of articles written by renowned experts
17 editions published between 2007 and 2009 in English and held by 220 WorldCat member libraries worldwide
Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. This volume summarises and reviews the consistent themes from his work through a series of articles written by renowned experts
Probability and phase transition by
Geoffrey Grimmett(
Book
)
8 editions published between 1994 and 2011 in English and held by 171 WorldCat member libraries worldwide
This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition
8 editions published between 1994 and 2011 in English and held by 171 WorldCat member libraries worldwide
This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition
Optimal stopping rules by
Alʹbert Nikolaevich Shiri︠a︡ev(
)
12 editions published in 2008 in English and held by 56 WorldCat member libraries worldwide
Although three decades have passed since first publication of this book reprinted now as a result of popular demand, the content remains uptodate and interesting for many researchers as is shown by the many references to it in current publications. The "ground floor" of Optimal Stopping Theory was constructed by A.Wald in his sequential analysis in connection with the testing of statistical hypotheses by nontraditional (sequential) methods. It was later discovered that these methods have, in idea, a close connection to the general theory of stochastic optimization for random processes. The area of application of the Optimal Stopping Theory is very broad. It is sufficient at this point to emphasise that its methods are well tailored to the study of American (type) options (in mathematics of finance and financial engineering), where a buyer has the freedom to exercise an option at any stopping time. In this book, the general theory of the construction of optimal stopping policies is developed for the case of Markov processes in discrete and continuous time. One chapter is devoted specially to the applications that address problems of the testing of statistical hypotheses, and quickest detection of the time of change of the probability characteristics of the observable processes. The author, A.N.Shiryaev, is one of the leading experts of the field and gives an authoritative treatment of a subject that, 30 years after original publication of this book, is proving increasingly important
12 editions published in 2008 in English and held by 56 WorldCat member libraries worldwide
Although three decades have passed since first publication of this book reprinted now as a result of popular demand, the content remains uptodate and interesting for many researchers as is shown by the many references to it in current publications. The "ground floor" of Optimal Stopping Theory was constructed by A.Wald in his sequential analysis in connection with the testing of statistical hypotheses by nontraditional (sequential) methods. It was later discovered that these methods have, in idea, a close connection to the general theory of stochastic optimization for random processes. The area of application of the Optimal Stopping Theory is very broad. It is sufficient at this point to emphasise that its methods are well tailored to the study of American (type) options (in mathematics of finance and financial engineering), where a buyer has the freedom to exercise an option at any stopping time. In this book, the general theory of the construction of optimal stopping policies is developed for the case of Markov processes in discrete and continuous time. One chapter is devoted specially to the applications that address problems of the testing of statistical hypotheses, and quickest detection of the time of change of the probability characteristics of the observable processes. The author, A.N.Shiryaev, is one of the leading experts of the field and gives an authoritative treatment of a subject that, 30 years after original publication of this book, is proving increasingly important
Percolatio by
Geoffrey Grimmett(
Book
)
1 edition published in 1989 in English and held by 29 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 29 WorldCat member libraries worldwide
Percolation theory at SaintFlour by
Geoffrey Grimmett(
Book
)
7 editions published in 2012 in English and held by 26 WorldCat member libraries worldwide
7 editions published in 2012 in English and held by 26 WorldCat member libraries worldwide
Lectures on probability theory and statistics : Ecole d'été de probabilités de SaintFlour XXVIII, 1998 by
Michel Emery(
Book
)
1 edition published in 1997 in English and held by 21 WorldCat member libraries worldwide
This volume contains lectures given at the SaintFlour Summer School of Probability Theory during 17th Aug.  3rd Sept. 1998. The contents of the three courses are the following:  Continuous martingales on differential manifolds.  Topics in nonparametric statistics.  Free probability theory. The reader is expected to have a graduate level in probability theory and statistics. This book is of interest to PhD students in probability and statistics or operators theory as well as for researchers in all these fields. The series of lecture notes from the SaintFlour Probability Summer School can be considered as an encyclopedia of probability theory and related fields
1 edition published in 1997 in English and held by 21 WorldCat member libraries worldwide
This volume contains lectures given at the SaintFlour Summer School of Probability Theory during 17th Aug.  3rd Sept. 1998. The contents of the three courses are the following:  Continuous martingales on differential manifolds.  Topics in nonparametric statistics.  Free probability theory. The reader is expected to have a graduate level in probability theory and statistics. This book is of interest to PhD students in probability and statistics or operators theory as well as for researchers in all these fields. The series of lecture notes from the SaintFlour Probability Summer School can be considered as an encyclopedia of probability theory and related fields
Mathematics of multiscale materials by
Kenneth M Golden(
)
2 editions published in 1998 in English and held by 20 WorldCat member libraries worldwide
Polycrystalline metals, porous rocks, colloidal suspensions, epitaxial thin films, gels, foams, granular aggregates, sea ice, shapememory metals, magnetic materials, and electrorheological fluids are all examples of materials where an understanding of the mathematics on the different length scales is a key to interpreting their physical behavior. In their analysis of these media, scientists coming from a number of disciplines have encountered similar mathematical problems, yet it is rare for researchers in the various fields to meet. The 19951996 program at the Institute for Mathematics and its Applications was devoted to Mathematical Methods in Material Science, and was attended by materials scientists, physicists, geologists, chemists engineers, and mathematicians. The present volume contains chapters which have emerged from four of the workshops held during the year, focusing on the following areas: Disordered Materials; Interfaces and Thin Films; Mechanical Response of Materials from Angstroms to Meters; and Phase Transformation, Composite Materials and Microstructure. The scales treated in these workshops ranged from the atomic to the microstructural to the macroscopic, the microstructures from ordered to random, and the treatments from "purely" theoretical to the highly applied. Taken together, these works form a compelling and broad account of many aspects of the science of multiscale materials, and will hopefully inspire research across the selfimposed barriers of twentieth century science
2 editions published in 1998 in English and held by 20 WorldCat member libraries worldwide
Polycrystalline metals, porous rocks, colloidal suspensions, epitaxial thin films, gels, foams, granular aggregates, sea ice, shapememory metals, magnetic materials, and electrorheological fluids are all examples of materials where an understanding of the mathematics on the different length scales is a key to interpreting their physical behavior. In their analysis of these media, scientists coming from a number of disciplines have encountered similar mathematical problems, yet it is rare for researchers in the various fields to meet. The 19951996 program at the Institute for Mathematics and its Applications was devoted to Mathematical Methods in Material Science, and was attended by materials scientists, physicists, geologists, chemists engineers, and mathematicians. The present volume contains chapters which have emerged from four of the workshops held during the year, focusing on the following areas: Disordered Materials; Interfaces and Thin Films; Mechanical Response of Materials from Angstroms to Meters; and Phase Transformation, Composite Materials and Microstructure. The scales treated in these workshops ranged from the atomic to the microstructural to the macroscopic, the microstructures from ordered to random, and the treatments from "purely" theoretical to the highly applied. Taken together, these works form a compelling and broad account of many aspects of the science of multiscale materials, and will hopefully inspire research across the selfimposed barriers of twentieth century science
Fundamentals of stochastic filtering by
Alan Bain(
)
3 editions published between 2008 and 2009 in English and held by 13 WorldCat member libraries worldwide
The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known KalmanBucy filter which has found widespread practical application. The purpose of this book is to provide a rigorous mathematical treatment of the nonlinear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient
3 editions published between 2008 and 2009 in English and held by 13 WorldCat member libraries worldwide
The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known KalmanBucy filter which has found widespread practical application. The purpose of this book is to provide a rigorous mathematical treatment of the nonlinear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient
Probability: An Introduction by
Geoffrey Grimmett(
Book
)
2 editions published in 2014 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 5 WorldCat member libraries worldwide
An Introduction by
Geoffrey Grimmett(
Book
)
1 edition published in 1986 in English and held by 5 WorldCat member libraries worldwide
A concise introduction to probability and random processes at firstdegree level with exercises and problems
1 edition published in 1986 in English and held by 5 WorldCat member libraries worldwide
A concise introduction to probability and random processes at firstdegree level with exercises and problems
Lectures on probability theory and statistics : Ecole d'été de probabilités de SaintFlour 26, 1996 by
Evarist Giné(
Book
)
1 edition published in 1997 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1997 in English and held by 4 WorldCat member libraries worldwide
Kakuritsuron nyūmon(
Book
)
2 editions published in 2004 in Japanese and held by 3 WorldCat member libraries worldwide
2 editions published in 2004 in Japanese and held by 3 WorldCat member libraries worldwide
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Related Identities
 Stirzaker, David
 Welsh, D. J. A. Honoree Dedicatee Editor
 Giné, Evarist 1944 Author
 SaloffCoste, L.
 Bernard, P. (Pierre) 1944 Editor
 Hammersley, J. M. (John Michael) Dedicatee
 McDiarmid, Colin Editor
 North Atlantic Treaty Organization Scientific Affairs Division
 Rozovskii, B. Author
 Shiryaev, Albert N. Author
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Associated Subjects
Brownian motion processes Chaotic behavior in systems ChemistryMathematics Combinatorial analysis Continuum mechanics Distribution (Probability theory) Economics Engineering Ferromagnetism Filters (Mathematics) Finance Global analysis (Mathematics) Global differential geometry Graph theory Ising model Lattice theory Length measurement Lévy processes MaterialsMathematical models Mathematical physics Mathematical statistics Mathematics Numerical analysis Optimal stopping (Mathematical statistics) Percolation (Statistical physics) Phase transformations (Statistical physics) Physics Probabilities Random walks (Mathematics) Rotational motion Sequential analysis Spatial analysis (Statistics) Statistical mechanics Statistics Stochastic processes Structural control (Engineering) Trees (Graph theory)