-
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...
-
作者：Osada, Hirofumi
作者单位：Kyushu University
-
作者：Gwynne, Ewain; Pfeffer, Joshua; Sheffield, Scott
作者单位：University of Chicago; Columbia University; Massachusetts Institute of Technology (MIT)
摘要：Recent works have shown that there is a canonical way to to assign a metric (distance function) to a Liouville quantum gravity (LQG) surface for any parameter gamma is an element of(0,2). We establish a strong confluence property for LQG geodesics, which generalizes a result proven by Angel, Kolesnik and Miermont for the Brownian map. Using this property, we also establish zero-one laws for the Hausdorff dimensions of geodesics, metric ball boundaries, and metric nets w.r.t. the Euclidean or L...
-
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 ...
-
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...
