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作者：Hermon, Jonathan; Salez, Justin
作者单位：University of Cambridge; Universite Paris Cite
摘要：We consider the zero-range process with arbitrary bounded monotone rates on the complete graph, in the regime where the number of sites diverges while the density of particles per site converges. We determine the asymptotics of the mixing time from any initial configuration, and establish the cutoff phenomenon. The intuitive picture is that the system separates into a slowly evolving solid phase and a quickly relaxing liquid phase: as time passes, the solid phase dissolves into the liquid phas...
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作者：Gwynne, Ewain; Holden, Nina; Miller, Jason
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The peanosphere construction of Duplantier, Miller and Sheffield provides a means of representing a gamma-Liouville quantum gravity (LQG) surface, gamma is an element of(0, 2), decorated with a space-filling form of Schramm's SLE kappa(,) kappa = 16/gamma(2) is an element of (4, infinity), eta as a gluing of a pair of trees which are encoded by a correlated two-dimensional Brownian motion Z. We prove a KPZ-type formula which relates the Hausdorff dimension of any Borel subset A of the range of...
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作者：Asselah, Amine; Schapira, Bruno
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite
摘要：We study scenarii linked with the Swiss cheese picture in dimension 3 obtained when two random walks are forced to meet often, or when one random walk is forced to squeeze its range. In the case of two random walks, we show that they most likely meet in a region of optimal density. In the case of one random walk, we show that a small range is reached by a strategy uniform in time. Both results rely on an original inequality estimating the cost of visiting sparse sites, and in the case of one r...
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作者：Lee, Jong Jun; Mueller, Carl; Neuman, Eyal
作者单位：University of Texas System; University of Texas Southwestern Medical Center; University of Rochester; Imperial College London
摘要：We consider a stochastic flow phi(t) (x, omega) in R-n with initial point phi(0)(x, omega) = x, driven by a single n-dimensional Brownian motion, and with an outward radial drift of magnitude F(parallel to phi(t)(x)parallel to/parallel to phi(t)(x)parallel to), with F nonnegative, bounded and Lipschitz. We consider initial points x lying in a set of positive distance from the origin. We show that there exist constants C*, c* > 0 not depending on n, such that if F > C* n then the image of the i...
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作者：Bates, Erik; Chatterjee, Sourav
作者单位：Stanford University; Stanford University
摘要：Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In this paper, we introduce some new computational tools that do not require integrability. We begin by defining a new kind of abstract limit object, called partitioned subprobability measure, to describe the limits of endpoint distributions of directed polymers. Inspired by a recent work of Mukherjee and Varadhan on larg...
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作者：Chatterjee, Sourav; Harel, Matan
作者单位：Stanford University; Tel Aviv University
摘要：We consider a random geometric graph G(chi(n), r(n)), given by connecting two vertices of a Poisson point process chi(n) of intensity n on the d-dimensional unit torus whenever their distance is smaller than the parameter r(n). The model is conditioned on the rare event that the number of edges observed, vertical bar E vertical bar, is greater than (1 + delta)E(vertical bar E vertical bar), for some fixed delta > 0. This article proves that upon conditioning, with high probability there exists...
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作者：Dette, Holger; Tomecki, Dominik; Venker, Martin
作者单位：Ruhr University Bochum
摘要：We investigate moment sequences of probability measures on subsets of the real line under constraints of certain moments being fixed. This corresponds to studying sections of nth moment spaces, that is, the spaces of moment sequences of order n. By equipping these sections with the uniform or more general probability distributions, we manage to give for large n precise results on the (probabilistic) barycenters of moment space sections and the fluctuations of random moments around these baryce...
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作者：Remy, Guillaume; Zhu, Tunan
作者单位：Columbia University; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider a subcritical Gaussian multiplicative chaos (GMC) measure defined on the unit interval [0, 1] and prove an exact formula for the fractional moments of the total mass of this measure. Our formula includes the case where log-singularities (also called insertion points) are added in 0 and 1, the most general case predicted by the Selberg integral. The idea to perform this computation is to introduce certain auxiliary functions resembling holomorphic observables of conformal field theo...
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作者：Schweiger, Florian
作者单位：University of Bonn
摘要：We show that the centred maximum of the four-dimensional membrane model on a box of sidelength N converges in distribution. To do so, we use a criterion of Ding, Roy and Zeitouni (Ann. Probab. 45 (2017) 3886-3928) and prove sharp estimates for the Green's function of the discrete Bilaplacian. These estimates are the main contribution of this work and might also be of independent interest. To derive them, we use estimates for the approximation quality of finite difference schemes as well as res...
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作者：Raoufi, Aran
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that at any inverse temperature beta and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. The theorem is equivalent with the differentiability of the free energy with respect to the temperature at any temperature. This is obtained for a general class of interactions, that is automorphism-invariant and irreducible coupling constants. The proof uses the random current represen...
