Borodin, Alexei
Overview
Works:  39 works in 45 publications in 1 language and 140 library holdings 

Roles:  Author, Thesis advisor 
Classifications:  QA613.8, 515.22 
Publication Timeline
.
Most widely held works by
Alexei Borodin
Representations of the infinite symmetric group by
Alexei Borodin(
Book
)
5 editions published between 2016 and 2017 in English and held by 55 WorldCat member libraries worldwide
5 editions published between 2016 and 2017 in English and held by 55 WorldCat member libraries worldwide
Transition between Airy1 and Airy2 processes and TASEP fluctuations(
)
1 edition published in 2007 in English and held by 7 WorldCat member libraries worldwide
We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions starting with certain deterministic initial conditions. F or large time $t$, one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy$_1$ and Airy$_2$ processes, whose onepoint distributions are the GOE and GUE TracyWidom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its onepoint distribution is a new interpolati on between GOE and GUE edge distributions
1 edition published in 2007 in English and held by 7 WorldCat member libraries worldwide
We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions starting with certain deterministic initial conditions. F or large time $t$, one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy$_1$ and Airy$_2$ processes, whose onepoint distributions are the GOE and GUE TracyWidom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its onepoint distribution is a new interpolati on between GOE and GUE edge distributions
Anisotropic growth of random surfaces in 2 + 1 dimensions(
)
1 edition published in 2008 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 7 WorldCat member libraries worldwide
Large time asymptotics of growth models on spacelike paths I: PushASEP(
)
1 edition published in 2007 in English and held by 7 WorldCat member libraries worldwide
We consider a new interacting particle system on the onedimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of the height function of the associated growth model along any spacelike path are described by the Airy$_1$ and Airy$_2$ processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases
1 edition published in 2007 in English and held by 7 WorldCat member libraries worldwide
We consider a new interacting particle system on the onedimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of the height function of the associated growth model along any spacelike path are described by the Airy$_1$ and Airy$_2$ processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases
Large time asymptotics of growth models on spacelike paths I: PushASEP by
Alexei Borodin(
Book
)
2 editions published in 2007 in English and held by 3 WorldCat member libraries worldwide
We consider a new interacting particle system on the onedimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of the height function of the associated growth model along any spacelike path are described by the Airy$_1$ and Airy$_2$ processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases
2 editions published in 2007 in English and held by 3 WorldCat member libraries worldwide
We consider a new interacting particle system on the onedimensional lattice that interpolates between TASEP and Toom's model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of the height function of the associated growth model along any spacelike path are described by the Airy$_1$ and Airy$_2$ processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle's trajectory as special cases
Free energy fluctuations for directed polymers in random media in 1 + 1 dimensions by
Alexei Borodin(
Book
)
1 edition published in 2012 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 3 WorldCat member libraries worldwide
Anisotropic growth of random surfaces in 2+1 dimensions by
Alexei Borodin(
Book
)
1 edition published in 2008 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 3 WorldCat member libraries worldwide
Transition between Airy1 and Airy2 processes and TASEP fluctuations by
Alexei Borodin(
Book
)
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
Large time asymptotics of growth models on spacelike paths II: PNG and parallel TASEP by
Alexei Borodin(
Book
)
2 editions published in 2007 in English and held by 3 WorldCat member libraries worldwide
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy$_1$ process. This result holds more generally for the observation points located along any spacelike path in the spacetime plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update
2 editions published in 2007 in English and held by 3 WorldCat member libraries worldwide
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy$_1$ process. This result holds more generally for the observation points located along any spacelike path in the spacetime plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update
Large time asymptotics of growth models on spacelike paths II: PNG and parallel TASEP(
)
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy$_1$ process. This result holds more generally for the observation points located along any spacelike path in the spacetime plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy$_1$ process. This result holds more generally for the observation points located along any spacelike path in the spacetime plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update
Harmonic analysis on the infinite symmetric group by
Alexei Borodin(
)
1 edition published in 2001 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 2 WorldCat member libraries worldwide
Limits of determinantal processes near a tacnode by
Alexei Borodin(
)
1 edition published in 2011 in Undetermined and held by 1 WorldCat member library worldwide
We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter ε > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ε ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ε ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process
1 edition published in 2011 in Undetermined and held by 1 WorldCat member library worldwide
We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter ε > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ε ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ε ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process
On adding a list of numbers (and other onedependent determinantal processes) by
Alexei Borodin(
)
1 edition published in 2010 in Undetermined and held by 1 WorldCat member library worldwide
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a onedependent determinantal point process. This makes it easy to answer natural questions: How many carries are typical? Where are they located? We show that many further examples, from combinatorics, algebra and group theory, have essentially the same neat formulae, and that any onedependent point process on the integers is determinantal. The examples give a gentle introduction to the emerging fields of onedependent and determinantal point processes
1 edition published in 2010 in Undetermined and held by 1 WorldCat member library worldwide
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a onedependent determinantal point process. This makes it easy to answer natural questions: How many carries are typical? Where are they located? We show that many further examples, from combinatorics, algebra and group theory, have essentially the same neat formulae, and that any onedependent point process on the integers is determinantal. The examples give a gentle introduction to the emerging fields of onedependent and determinantal point processes
Representations of the infinite symmetric group by
Alexei Borodin(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and selfcontained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and selfcontained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas
Limits of detenninantal processes near a tacnode by
Alexei Borodin(
)
1 edition published in 2011 in Undetermined and held by 1 WorldCat member library worldwide
We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter ε > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ε ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ε ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process
1 edition published in 2011 in Undetermined and held by 1 WorldCat member library worldwide
We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter ε > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ε ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ε ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process
Markov processes on the path space of the Gelfand–Tsetlin graph and on its boundary by
Alexei Borodin(
)
1 edition published in 2012 in Undetermined and held by 1 WorldCat member library worldwide
We construct a fourparameter family of Markov processes on infinite Gelfand–Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinitedimensional boundary of the Gelfand–Tsetlin graph or, equivalently, the space of extreme characters of the infinitedimensional unitary group U(∞). The process has a unique invariant distribution which arises as the decomposing measure in a natural problem of harmonic analysis on U(∞) posed in Olshanski (2003) [44]. As was shown in Borodin and Olshanski (2005) [11], this measure can also be described as a determinantal point process with a correlation kernel expressed through the Gauss hypergeometric function
1 edition published in 2012 in Undetermined and held by 1 WorldCat member library worldwide
We construct a fourparameter family of Markov processes on infinite Gelfand–Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinitedimensional boundary of the Gelfand–Tsetlin graph or, equivalently, the space of extreme characters of the infinitedimensional unitary group U(∞). The process has a unique invariant distribution which arises as the decomposing measure in a natural problem of harmonic analysis on U(∞) posed in Olshanski (2003) [44]. As was shown in Borodin and Olshanski (2005) [11], this measure can also be described as a determinantal point process with a correlation kernel expressed through the Gauss hypergeometric function
Infinitedimensional diffusions as limits of random walks on partitions by
Alexei Borodin(
)
1 edition published in 2009 in Undetermined and held by 1 WorldCat member library worldwide
Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n → ∞, a family of infinitedimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the socalled zmeasures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described
1 edition published in 2009 in Undetermined and held by 1 WorldCat member library worldwide
Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n → ∞, a family of infinitedimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the socalled zmeasures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described
Asymptotics of Plancherel measures for the infinitedimensional unitary group by
Alexei Borodin(
)
1 edition published in 2008 in Undetermined and held by 1 WorldCat member library worldwide
We study a twodimensional family of probability measures on infinite GelfandTsetlin schemes induced by a distinguished family of extreme characters of the infinitedimensional unitary group. These measures are unitary group analogs of the wellknown Plancherel measures for symmetric groups. We show that any measure from our family defines a determinantal point process on Z_+ x Z, and we prove that in appropriate scaling limits, such processes converge to two different extensions of the discrete sine process as well as to the extended Airy and Pearcey processes
1 edition published in 2008 in Undetermined and held by 1 WorldCat member library worldwide
We study a twodimensional family of probability measures on infinite GelfandTsetlin schemes induced by a distinguished family of extreme characters of the infinitedimensional unitary group. These measures are unitary group analogs of the wellknown Plancherel measures for symmetric groups. We show that any measure from our family defines a determinantal point process on Z_+ x Z, and we prove that in appropriate scaling limits, such processes converge to two different extensions of the discrete sine process as well as to the extended Airy and Pearcey processes
Harmonic Functions on Multiplicative Graphs and Interpolation Polynomials by
Alexei Borodin(
)
1 edition published in 2000 in Undetermined and held by 1 WorldCat member library worldwide
We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on multivariate interpolation polynomials associated with Schur's S and P functions and with Jack symmetric functions. As a byproduct, we compute certain Selbergtype integrals
1 edition published in 2000 in Undetermined and held by 1 WorldCat member library worldwide
We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on multivariate interpolation polynomials associated with Schur's S and P functions and with Jack symmetric functions. As a byproduct, we compute certain Selbergtype integrals
On a conjecture of Widom by
Alexei Borodin(
)
1 edition published in 2006 in Undetermined and held by 1 WorldCat member library worldwide
We prove a conjecture of Widom (2002 Int. Math. Res. Not. 455–64 (Preprint math/0108008)) about the reality of eigenvalues of certain infinite matrices arising in asymptotic analysis of large Toeplitz determinants. As a byproduct, we obtain a new proof of Okounkov's formula for the (determinantal) correlation functions of the Schur measures on partitions
1 edition published in 2006 in Undetermined and held by 1 WorldCat member library worldwide
We prove a conjecture of Widom (2002 Int. Math. Res. Not. 455–64 (Preprint math/0108008)) about the reality of eigenvalues of certain infinite matrices arising in asymptotic analysis of large Toeplitz determinants. As a byproduct, we obtain a new proof of Okounkov's formula for the (determinantal) correlation functions of the Schur measures on partitions
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Aleksej Borodin
Alexei Borodin mathématicien russe
Alexei Borodin RussianAmerican mathematician
Alexei Borodin Russisch wiskundige
Alexei Borodin russischer Mathematiker
Borodin, A. M.
Borodin, Aleksej 1975
Borodin, Aleksej Michajlovič 1975
Borodin, Alexei.
Бородин, Алексей Михайлович
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