Fluctuations of particle systems determined by Schur generating functions
TLDR
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.About:
This article is published in Advances in Mathematics.The article was published on 2018-11-07 and is currently open access. It has received 69 citations till now. The article focuses on the topics: Schur's theorem & Schur product theorem.read more
Citations
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Journal ArticleDOI
Gaussian asymptotics of discrete $\beta$-ensembles
TL;DR: In this paper, the global fluctuations of particle ensembles are asymptotically Gaussian as the number of particles in the ensemble grows with the number n. The covariance is universal and coincides with its counterpart in random matrix theory.
Journal ArticleDOI
Asymptotics of random domino tilings of rectangular Aztec diamonds
Alexey Bufetov,Alisa Knizel +1 more
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.
Journal ArticleDOI
Fourier transform on high-dimensional unitary groups with applications to random tilings
Alexey Bufetov,Vadim Gorin +1 more
TL;DR: In this article, a combination of direct and inverse Fourier transforms on the unitary group U(N) identifies normalized characters with probability measures on N-tuples of integers.
Journal ArticleDOI
Crystallization of Random Matrix Orbits
TL;DR: In this paper, it was shown that for a uniformly-random self-adjoint matrix with fixed eigenvalues, the eigenvalue of the principal corners of the matrix crystallizes on the irregular lattice of all the roots of derivatives of a single polynomial.
MonographDOI
Lectures on Random Lozenge Tilings
TL;DR: The author explains each feature of random tilings of large domains, discussing several different points of view and leading on to open problems in the field, as well as serving as a self-contained introduction to the subject.
References
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TL;DR: In this article, the authors discuss the relationship between Markov Processes and Ergodic properties of Markov processes and their relation with PDEs and potential theory. But their main focus is on the convergence of random processes, measures, and sets.
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TL;DR: Weyl as discussed by the authors discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations using basic concepts from algebra, and examines the various properties of the groups.