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作者：O'Connell, Neil
作者单位：University College Dublin
摘要：We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure. These are related to K-Bessel functions of matrix argument and multivariate generalisations of these functions. The latter are eigenfunctions of a particular quantisation of the non-Abelian Toda lattice.
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作者：Kim, Seonwoo
作者单位：Seoul National University (SNU)
摘要：We investigate the second time scale of the metastable behavior of the reversible inclusion process in an extension of the study by Bianchi et al. (Electron J Probab 22:1-34, 2017), which presented the first time scale of the same model and conjectured the scheme of multiple time scales. We show that N/d(N)(2) is indeed the correct second time scale for the most general class of reversible inclusion processes, and thus prove the first conjecture of the foresaid study. Here, N denotes the numbe...
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作者：Biskup, Marek; Chen, Xin; Kumagai, Takashi; Wang, Jian
作者单位：University of California System; University of California Los Angeles; Shanghai Jiao Tong University; Kyoto University; Fujian Normal University; Fujian Normal University; Fujian Normal University
摘要：We study random walks on Z(d) (with d >= 2) among stationary ergodic random conductances {C-x,C-y : x, y is an element of Z(d)} that permit jumps of arbitrary length. Our focus is on the quenched invariance principle (QIP) which we establish by a combination of corrector methods, functional inequalities and heat-kernel technology assuming that the p-th moment of Sigma(x is an element of Zd) C-0,C-x vertical bar x vertical bar(2) and q-th moment of 1/C-0,C-x for x neighboring the origin are fin...
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作者：Najnudel, Joseph; Virag, Balint
作者单位：University of Bristol; University of Toronto
摘要：The bead process introduced by Boutillier is a countable interlacing of the Sine(2) point processes. We construct the bead process for general Sine(beta) processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite beta corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to...
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作者：Dimitrov, Evgeni; Wu, Xuan
作者单位：Columbia University; University of Chicago
摘要：In this paper we prove an analogue of the Komlos-Major-Tusnady (KMT) embedding theorem for random walk bridges. The random bridges we consider are constructed through random walks with i.i.d jumps that are conditioned on the locations of their endpoints. We prove that such bridges can be strongly coupled to Brownian bridges of appropriate variance when the jumps are either continuous or integer valued under some mild technical assumptions on the jump distributions. Our arguments follow a simil...
