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作者：Bertacco, Federico; Gwynne, Ewain; Sheffield, Scott
作者单位：Imperial College London; University of Chicago; Massachusetts Institute of Technology (MIT)
摘要：The Smith embedding of a finite planar map with two marked vertices, possibly with conductances on the edges, is a way of representing the map as a tiling of a finite cylinder by rectangles. In this embedding, each edge of the planar map corresponds to a rectangle, and each vertex corresponds to a horizontal segment. Given a sequence of finite planar maps embedded in an infinite cylinder such that the random walk on both the map and its planar dual converges to Brownian motion modulo time chan...
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作者：Schapira, Bruno; Valesin, Daniel
作者单位：Aix-Marseille Universite; University of Warwick
摘要：We study the contact process on a dynamic random d-regular graph with an edge-switching mechanism as well as an interacting particle system that arises from the local description of this process called the herds process. Both these processes were introduced in (da Silva, Oliveira and Valesin (2021)); there it was shown that the herds process has a phase transition with respect to the infectivity parameter lambda, depending on the parameter v that governs the edge dynamics. Improving on a resul...
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作者：Dubroff, Quentin; Kahn, Jeff
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Proving a 2009 conjecture of Itai Benjamini, we show: Theorem. For any C there is an epsilon > 0 such that for any simple graph G on V of size n, and X-0, ... an ordinary random walk on G, P ({ X- 0 ,...,X (C n )} = V ) < e (- epsilon n) . A first ingredient in the proof of this is a similar statement for Markov chains in which all transition probabilities are sufficiently small relative to C .
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作者：Ransford, Julian
作者单位：University of Toronto
摘要：Krishnan and Quastel (Ann. Appl. Probab. 28 (2018) 3736-3764) showed that the fluctuations of Sepp & auml;l & auml;inen's log-gamma polymer converge in law to the Tracy-Widom GUE distribution in the intermediate disorder regime. This regime corresponds to taking the inverse temperature beta to depend on the length of the polymer 2n, with beta = n(-alpha) for some alpha < 1/4. They also conjectured that this should hold for directed polymers with general i.i.d weights. We prove that their conje...
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作者：Chatzigeorgiou, Georgiana; Morfe, Peter; Otto, Felix; Wang, Lihan
作者单位：Max Planck Society
摘要：We analyze the large-time asymptotics of a passive tracer with drift equal to the curl of the Gaussian free field in two dimensions with ultra-violet cutoff at scale unity. We prove that the mean-squared displacement scales like t root lnt, as predicted in the physics literature. This improves the asymptotics recently established in recent work of Cannizzaro, Haunschmidt-Sibitz, and Toninelli (Ann. Probab. 50 (2022) 2475-2498), which uses mathematical-physics type analysis in Fock space. Our a...
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作者：Chen, Zhen-Qing; Wang, Jie-Ming
作者单位：University of Washington; University of Washington Seattle; Beijing Institute of Technology; Beijing Institute of Technology
摘要：In this paper a necessary and sufficient condition is obtained for the scale invariant boundary Harnack principle (BHP in abbreviation) for a large class of Hunt processes on metric measure spaces that are in weak duality with another Hunt process. We then apply it to a class of discontinuous subordinate Brownian motions with Gaussian components in Wdfor which the L & eacute;vy density of the subordinators satisfies some mild comparability condition. We show that the scale invariant BHP holds ...
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作者：Schertzer, Emmanuel; Tourniaire, Julie
作者单位：University of Vienna; Universite Marie et Louis Pasteur; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift-mu and killed upon reaching 0. More precisely, the particles branch at rate r(x) = (1 + W (x))/2, where W is a compactly supported and nonnegative smooth function and the drift mu is chosen in such a way that the system is critical in some sense. This particle system can be seen as an analytically tractable model for fluctuating fronts, describing ...
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作者：Dagallier, Benoit
作者单位：New York University
摘要：We consider the weakly asymmetric simple exclusion process on a ring, driven out of equilibrium by tilting the dynamics so as to enforce a macroscopic current of particles on a large time interval. In this current-biased dynamics, the tilt by the current makes the dynamics nonlocal, nonhomogeneous and induces long-range correlations. We compute the correlation structure in the large time, large size limit for a certain range of asymmetry and current strength, recovering heuristic results of Bo...
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作者：Li, Jhih-huang; Saenz, Axel
作者单位：National Taiwan University; Oregon State University
摘要：We give contour integral formulas for the generating function of the joint distribution of the PushASEP on a ring. We obtained these formulas through a rigorous treatment of Bethe ansatz. The approach relies on residue computations and controlling the location of the Bethe roots, which we achieve by partially decoupling the Bethe equations and extending the system of equations. Moreover, we are able to use our formulas to compute the asymptotic fluctuations for the flat and step initial condit...
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作者：Catellier, Remi; Duboscq, Romain
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely nondeterminism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion B(H )for H > (1) (4), we prove that the drift may be taken to be kappa > 0 H & ouml;lder continuous and bounded for kappa > (3)(2) - (1) (2H) ...
