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作者：Aoun, Richard; Sert, Cagri
作者单位：New York University; New York University Abu Dhabi; University of Zurich
摘要：The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space M, we obtain explicit bounds that depend only on M, the size of support of the measure as in the classical case of sums of independent random variables, and on the norm of the driving probability measure in the left regular representation of the group of isometries...
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作者：Liu, Zhipeng
作者单位：University of Kansas
摘要：We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one-point distribution of the geodesic location joint with the last passage times, and its limit as the parameters go to infinity under the KPZ scaling.
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作者：Bufetov, Alexey; Nejjar, Peter
作者单位：Leipzig University; University of Bonn; University of Bonn
摘要：This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length N. Our main result is that for particle densities in (0, 1), the total-variation cutoff window of ASEP is N-1/3 and the cutoff profile is 1 - F-GUE, where F-GUE is the Tracy-Widom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbe and Lacoin. Our proof combines coupling arguments, the result of Tracy-Widom about fluctuations of ASEP starte...
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作者：Deuschel, Jean-Dominique; Guo, Xiaoqin
作者单位：Technical University of Berlin; University of Wisconsin System; University of Wisconsin Madison; University System of Ohio; University of Cincinnati
摘要：We prove a quenched local central limit theorem for continuous-time random walks in Z(d), d >= 2, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian upper and lower bounds for quenched and (positive and negative) moment estimates of the transition probabilities and asymptotics of the discrete Green's function.
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作者：Miclo, Laurent
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS)
摘要：Consider finite state space irreducible and absorbing Markov processes. A general spectral criterion is provided for the absorbing time to be close to an exponential random variable, whatever the starting point. When exiting points are added to the state space, our criterion also insures that the exit time and position are almost independent. Since this is valid for any exiting extension of the state space, it corresponds to an instance of the metastability phenomenon. Simple examples at small...
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作者：Osada, Hirofumi
作者单位：Kyushu University
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Cambridge; Imperial College London
摘要：We investigate level sets of the Gaussian free field on continuous transient metric graphs g and study the capacity of its level set clusters. We prove, without any further assumption on the base graph G, that the capacity of sign clusters on (G) over tilde is finite almost surely. This leads to a new and effective criterion to determine whether the sign clusters of the free field on (G) over tilde are bounded or not. It also elucidates why the critical parameter for percolation of level sets ...
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作者：Sly, Allan; Sun, Nike; Zhang, Yumeng
作者单位：Princeton University; Massachusetts Institute of Technology (MIT); Stanford University
摘要：Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems. In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming predictions of statistical physics. Here we revisit one of these models, random regular k-nae-sat: knowing the satisfiability threshold, it is natural to study, in the satisfiable regime, the number of solutions in a typical instance. We prove here that the...
