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作者：Zhang, Lingfu
作者单位：University of California System; University of California Davis
摘要：We consider the Metropolis biased card shuffling (also called the multispecies ASEP on a finite interval or the random Metropolis scan). Its convergence to stationarity was believed to exhibit a total -variation cutoff, and that was proved a few years ago by Labbe and Lacoin (Ann. Probab. 47 (2019) 1541-1586). In this paper, we prove that (for N cards) the cutoff window is in the order of N1/3, and the cutoff profile is given by the Tracy-Widom GOE distribution function. This confirms a conjec...
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作者：Adamczak, Radoslaw; Pivovarov, Peter; Simanjuntak, Paul
作者单位：University of Warsaw; University of Missouri System; University of Missouri Columbia
摘要：We establish central limit theorems for the volumes of intersections of Bpn (the unit ball of in p) with uniform random subspaces of codimension d for fixed d and n -> infinity. As a corollary we obtain higher-order approximations for expected volumes, refining previous results by Koldobsky and Lifschitz and approximations obtained from the Eldan-Klartag version of CLT for convex bodies. We also obtain a central limit theorem for the Minkowski functional of the intersection body of Bnp, evalua...
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作者：Chen, Xin; Wang, Jian
作者单位：Shanghai Jiao Tong University; Fujian Normal University
摘要：Consider the Schrodinger operator L-V = - Delta + V on R-d , where V : R-d -> [0 , infinity) is a nonnegative and locally bounded potential on R-d so that for all x is an element of R-d with | x | >= 1, c(1)g( | x | ) <= V (x) <= c(2)g( | x | ) with some constants c 1 , c(2) > 0 and a nondecreasing and strictly positive function g : [0,infinity) -> [1 ,+infinity ) that satisfies g(2r) <= c(0)g(r) for all r > 0 and lim(r ->infinity )g(r) = infinity . We establish global in time and qualitativel...
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作者：Lipnowski, Michael; Wright, Lex
作者单位：University System of Ohio; Ohio State University; University of Michigan System; University of Michigan
摘要：We show that the Weil-Petersson probability that a random surface has first eigenvalue of the Laplacian less than 3/16-epsilon goes to zero as the genus goes to infinity.
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作者：Barnes, Clayton; Mytnik, Leonid; Sun, Zhenyao
作者单位：Technion Israel Institute of Technology; Beijing Institute of Technology
摘要：Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model the total occupation measure is known to have a continuously differentiable density (l(x))(x is an element of R), and we write (l(x))(x is an element of R )for its derivative. Although the process (l(x))(x >= 0) is not Markov, we prove that the pair(l(x), l(x))(x >= 0 )is a time-homogeneous Markov proc...
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作者：Berestycki, Julien; Kim, Yujin h.; Lubetzky, Eyal; Mallein, Bastien; Zeitouni, Ofer
作者单位：University of Oxford; University of Oxford; New York University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a branching Brownian motion in Rd with d >= 1 in which the position X(u) t is an element of Rd of a particle u at time t can be encoded by its direction theta(u) t is an element of Sd-1 and its distance R(u) t to 0. We prove that the extremal point process Sigma delta(theta(u) t,Rt(u)-m(d) t ) (where the sum is over all particles alive at time t and m(d) t is an explicit centering term) converges in distribution to a randomly shifted, decorated Poisson point process on Sd-1 x R. Mo...
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作者：Bauerschmidt, Roland; Park, Jiwoon; Rodriguez, Pierre-Francois
作者单位：University of Cambridge; Imperial College London
摘要：The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions and at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean is a multiple of the Gaussian free field. This article is the second in a series on the Discrete Gaussian model, extending the methods of the first paper by the analysis of general external fields (rather than macroscopic test functions on the torus). As ...
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作者：Bou-Rabee, Ahmed; Gwynne, Ewain
作者单位：New York University; University of Chicago
摘要：We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. The limit is a LQG harmonic ball, which we constructed in a companion paper. We also prove an analogous result for the divisible sandpile.
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作者：Chapuy, Guillaume; Louf, Baptiste; Walsh, Harriet
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Uppsala University; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We study the asymptotic behaviour of random integer partitions under a new probability law that we introduce, the Plancherel-Hurwitz measure. This distribution, which has a natural definition in terms of Young tableaux, is a deformation of the classical Plancherel measure, which appears naturally in the context of Hurwitz numbers, enumerating certain transposition factorisations in symmetric groups. We study a regime in which the number of factors in the underlying factorisations grows linearl...
