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作者：Herr, Sebastian; Roeckner, Michael; Spitz, Martin; Zhang, Deng
作者单位：University of Bielefeld; Shanghai Jiao Tong University
摘要：We study the three-dimensional stochastic Zakharov system in the energy space, where the Schr & ouml;dinger equation is driven by linear multiplicative noise and the wave equation is driven by additive noise. We prove the well-posedness of the system up to the maximal existence time and provide a blow-up alternative. We further show that the solution exists at least as long as it remains below the ground state. Two main ingredients of our proof are refined rescaling transformations and the nor...
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作者：Ang, Morris; Sun, Xin; Yu, Pu; Zhuang, Zijie
作者单位：University of California System; University of California San Diego; Peking University; Massachusetts Institute of Technology (MIT); University of Pennsylvania
摘要：The conformal loop ensemble (CLE) has two phases: for kappa E (8/3, 4], the loops are simple and do not touch each other or the boundary; for kappa E (4, 8), the loops are nonsimple and may touch each other and the boundary. For kappa E (4, 8), we derive the probability that the loop surrounding a given point touches the domain boundary. We also obtain the law of the conformal radius of this loop seen from the given point conditioned on the loop touching the boundary or not, refining a result ...
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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：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：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：De Vecchi, Francesco C.; Fresta, Luca; Gubinelli, Massimiliano
作者单位：University of Pavia; University of Bonn; University of Bonn; University of Oxford
摘要：Building on previous work on the stochastic analysis for Grassmann random variables, we introduce a forward-backward stochastic differential equation (FBSDE), which provides a stochastic quantisation of Grassmann measures. Our method is inspired by the so-called continuous renormalisation group, but avoids the technical difficulties encountered in the direct study of the flow equation for the effective potentials. As an application, we construct a family of weakly coupled subcritical Euclidean...
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作者：Mossel, Elchanan; Sly, Allan; Sohn, Youngtak
作者单位：Massachusetts Institute of Technology (MIT); Princeton University
摘要：In this paper we continue to rigorously establish the predictions in ground breaking work in statistical physics by Decelle, Krzakala, Moore, Zdeborov & aacute; (Phys. Rev. E 84 (2011) 066106) regarding the block model, in particular, in the case of q = 3 and q =4 communities. We prove that, for q = 3 and q = 4, there is no computational-statistical gap if the average degree is above some constant by showing it is information theoretically impossible to detect below the Kesten-Stigum bound. Th...
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作者：Qin, Shuo
作者单位：New York University
摘要：We prove a conjecture by Bertoin that the multidimensional elephant random walk on Zd is transient in dimensions d >= 3. We show that it undergoes a phase transition in dimensions d = 1, 2 between recurrence and transience at p = (2d + 1)/(4d).
