Probability Theory and Related Fields

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• Anomalous diffusion of random walk on random planar maps AI翻译
  作者：Gwynne, Ewain; Hutchcroft, Tom
  作者单位：University of Cambridge
  摘要：We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most n(1/4+on)(1) in n units of time. Together with the complementary lower bound proven by Gwynne and Miller (2017) this shows that the typical graph distance displacement of the walk after n steps is n(1/4+on) (1), as conjectured by Benjamini and Curien (Geom Funct Anal 2(2):501-531, 2013. arXiv:1202.5454). More generally, we show that the simple random walks on a cert...
• Bessel SPDEs and renormalised local times AI翻译
  作者：Altman, Henri Elad; Zambotti, Lorenzo
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite
  摘要：In this article, we prove integration by parts formulae (IbPFs) for the laws of Bessel bridges from 0 to 0 over the interval [0, 1] of dimension smaller than 3. As an application, we construct a weak version of a stochastic PDE having the law of a one-dimensional Bessel bridge (i.e. the law of a reflected Brownian bridge) as reversible measure, the dimension 1 being particularly relevant in view of applications to scaling limits of dynamical critical pinning models. We also exploit the IbPFs t...
• Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure AI翻译
  作者：Imamura, Takashi; Mucciconi, Matteo; Sasamoto, Tomohiro
  作者单位：Chiba University; Institute of Science Tokyo; Tokyo Institute of Technology
  摘要：In this paper we consider the Higher Spin Six Vertex Model on the lattice Z >= 2xZ >= 1. We first identify a family of translation invariant measures and subsequently we study the one point distribution of the height function for the model with certain random boundary conditions. Exact formulas we obtain prove to be useful in order to establish the asymptotic of the height distribution in the long space-time limit for the stationary Higher Spin Six Vertex Model. In particular, along the charac...
• Universality for critical KCM: infinite number of stable directions AI翻译
  作者：Hartarsky, Ivailo; Mareche, Laure; Toninelli, Cristina
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
  摘要：Kinetically constrained models (KCM) are reversible interacting particle systems on Z(d) with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automatawith random initial state known as U-bootstrap percolation. KCM have an interest in their own right, owing to their use for modelling the liquid-glass transition in condensed matter physics. In two dimensions there are three classes of models with qualitatively different s...
• Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications AI翻译
  作者：Chen, Xiaohui; Kato, Kengo
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Cornell University
  摘要：This paper is concerned with finite sample approximations to the supremum of a non-degenerate U-process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the U-process itself is not weakly convergent as a process. Such situations arise in a variety of modern statistical problems. We first consider Gaussian approximations, namely, approximate the U-process sup...
• Non-intersection of transient branching random walks AI翻译
  作者：Hutchcroft, Tom
  作者单位：University of Cambridge
  摘要：Let G be a Cayley graph of a nonamenable group with spectral radius rho<1. It is known that branching random walk on G with offspring distribution mu is transient, i.e., visits the origin at most finitely often almost surely, if and only if the expected number of offspring mu over bar satisfies mu over bar <=rho-1. Benjamini and Muller (Groups Geom Dyn, 6:231-247, 2012) conjectured that throughout the transient supercritical phase 1
• Entropic repulsion for the Gaussian free field conditioned on disconnection by level-sets AI翻译
  作者：Chiarini, Alberto; Nitzschner, Maximilian
  作者单位：University of California System; University of California Los Angeles; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We investigate level-set percolation of the discrete Gaussian free field on Zd, d = 3, in the strongly percolative regime. We consider the event that the level-set of theGaussian free field below a level a disconnects the discrete blow-up of a compact set A. Rd from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of theGaussian free field deviate from a specific multiple of the harmonic potential of A, when disconne...
• Weak LQG metrics and Liouville first passage percolation AI翻译
  作者：Dubedat, Julien; Falconet, Hugo; Gwynne, Ewain; Pfeffer, Joshua; Sun, Xin
  作者单位：Columbia University; University of Cambridge; Massachusetts Institute of Technology (MIT)
  摘要：For gamma is an element of (0, 2), we define a weak gamma-Liouville quantum gravity (LQG) metric to be a function h -> D-h which takes in an instance of the planar Gaussian free field and outputs a metric on the plane satisfying a certain list of natural axioms. We showthat these axioms are satisfied for any subsequential limits of Liouville first passage percolation. Such subsequential limits were proven to exist by Ding et al. (Tightness of Liouville first passage percolation for gamma is an...
• Noise sensitivity and exceptional times of transience for a simple symmetric random walk in one dimension AI翻译
  作者：Prigent, Martin; Roberts, Matthew I.
  作者单位：University of Bath
  摘要：We define a dynamical simple symmetric random walk in one dimension, and show that there almost surely exist exceptional times at which the walk tends to infinity. This is in contrast to the usual dynamical simple symmetric random walk in one dimension, for which such exceptional times are known not to exist. In fact we show that the set of exceptional times has Hausdorff dimension 1/2 almost surely, and give bounds on the rate at which the walk diverges at such times. We also show noise sensi...
• Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model (vol 173, pg 1349, 2019) AI翻译
  作者：Merkl, Franz; Rolles, Silke W. W.; Tarres, Pierre
  作者单位：University of Munich; Technical University of Munich; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite PSL; Universite Paris-Dauphine
  摘要：In the original publication, Acknowledgements section was incorrect. The correct Acknowledgements is given below.