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Alexey Bufetov

Bio: Alexey Bufetov is an academic researcher from University of Bonn. The author has contributed to research in topics: Unitary group & Symmetric group. The author has an hindex of 16, co-authored 41 publications receiving 666 citations. Previous affiliations of Alexey Bufetov include Massachusetts Institute of Technology & Russian Academy of Sciences.

Papers
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Journal ArticleDOI
TL;DR: In this paper, a new toolbox for the analysis of the global behavior of stochastic discrete particle systems has been developed, based on the notion of the Schur generating function of a random discrete configuration.

69 citations

Journal ArticleDOI
TL;DR: In this article, asymptotics of a domino tiling model on a class of domains which are called rectangular Aztec diamonds are considered and the Law of Large Numbers for the corresponding height functions and explicit formulas for the limit are provided.
Abstract: We consider asymptotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions and provide explicit formulas for the limit. For a special class of examples, the explicit parametrization of the frozen boundary is given. It turns out to be an algebraic curve with very special properties. Moreover, we establish the convergence of the fluctuations of the height functions to the Gaussian Free Field in appropriate coordinates. Our main tool is a recently developed moment method for discrete particle systems.

53 citations

Journal ArticleDOI
TL;DR: In this article, the Law of Large Numbers for the random counting measures describing the decomposition of a tensor product was proved for all series of classical Lie groups as the rank of the group goes to infinity, leading to two operations on measures which are deformations of the notions of free convolution and the free projection.
Abstract: We study the decompositions into irreducible components of tensor products and restrictions of irreducible representations for all series of classical Lie groups as the rank of the group goes to infinity. We prove the Law of Large Numbers for the random counting measures describing the decomposition. This leads to two operations on measures which are deformations of the notions of the free convolution and the free projection. We further prove that if one replaces counting measures with others coming from the work of Perelomov and Popov on the higher order Casimir operators for classical groups, then the operations on the measures turn into the free convolution and projection themselves. We also explain the relation between our results and limit shape theorems for uniformly random lozenge tilings with and without axial symmetry.

53 citations

Posted Content
TL;DR: In this paper, it was shown that the joint distribution of the values of the height function for the stochastic six vertex model in a quadrant along a down-right path coincides with that for the lengths of the first columns of partitions distributed according to certain Hall-Littlewood processes.
Abstract: We prove that the joint distribution of the values of the height function for the stochastic six vertex model in a quadrant along a down-right path coincides with that for the lengths of the first columns of partitions distributed according to certain Hall-Littlewood processes. In the limit when one of the quadrant axes becomes continuous, we also show that the two-dimensional random field of the height function values has the same distribution as the lengths of the first columns of partitions from certain ascending Hall-Littlewood processes evolving under a Robinson-Schensted-Knuth type Markovian evolution.

45 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the partition function of two versions of the continuum directed polymer in 1 + 1 dimension, and derived exact formulas for the Laplace transforms of the partition functions.

44 citations


Cited by
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Book ChapterDOI
01 Jan 2011
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

3,554 citations

01 Aug 1993
TL;DR: One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References as discussed by the authors
Abstract: One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.

1,491 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied a random Groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process and showed that shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.
Abstract: We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

1,031 citations

01 Jan 2016
TL;DR: The reflection groups and coxeter groups is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
Abstract: Thank you for downloading reflection groups and coxeter groups. Maybe you have knowledge that, people have search numerous times for their favorite books like this reflection groups and coxeter groups, but end up in malicious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they cope with some infectious bugs inside their computer. reflection groups and coxeter groups is available in our digital library an online access to it is set as public so you can download it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the reflection groups and coxeter groups is universally compatible with any devices to read.

450 citations

Book ChapterDOI
01 Jul 2004

370 citations