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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...
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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...
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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...
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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.
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作者：Eldan, Ronen
作者单位：Weizmann Institute of Science
摘要：The analysis of various models in statistical physics relies on the existence of decompositions of measures into mixtures of product-like components, where the goal is to attain a decomposition into measures whose entropy is close to that of the original measure, yet with small correlations between coordinates. We prove a related general result: For every measure mu on Rn and every epsilon>0, there exists a decomposition mu=integral mu theta dm(theta) such that H(mu)-E theta similar to mH(mu t...
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作者：Miller, Jason; Qian, Wei
作者单位：University of Cambridge
摘要：We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of SLE kappa. These hypotheses are satisfied by the LQG metric for gamma = root 8/3 constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each gamma is an element of (0, 2...
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作者：Caputo, Pietro; Quattropani, Matteo
作者单位：Roma Tre University
摘要：We consider sparse digraphs generated by the configuration model with given in-degree and out-degree sequences. We establish that with high probability the cover time is linear up to a poly-logarithmic correction. For a large class of degree sequences we determine the exponent gamma >= 1 of the logarithm and show that the cover time grows as n log(gamma) (n), where n is the number of vertices. The results are obtained by analysing the extremal values of the stationary distribution of the digra...
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作者：Gwynne, Ewain; Holden, Nina; Sun, Xin
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
摘要：We introduce a general technique for proving estimates for certain random planar maps which belong to the gamma-Liouville quantum gravity (LQG) universality class for gamma is an element of(0,2) The family of random planar maps we consider are those which can be encoded by a two-dimensional random walk with i.i.d. increments via a mating-of-trees bijection, and includes the uniform infinite planar triangulation (UIPT;gamma=8/3and planar maps weighted by the number of different spanning trees (...
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作者：Dunlap, Alexander; Gu, Yu; Ryzhik, Lenya; Zeitouni, Ofer
作者单位：Stanford University; Carnegie Mellon University; Weizmann Institute of Science
摘要：We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in d >= 3 with a small coupling constant, driven by a white in time and colored in space noise, are given by the Edwards-Wilkinson model. This gives an alternative proof, that avoids perturbation expansions, to the results of Magnen and Unterberger (J Stat Phys 171:543-598, 2018).
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作者：Holmes, Mark; Perkins, Edwin
作者单位：University of Melbourne; University of British Columbia
摘要：We investigate the scaling limit of the range (the set of visited vertices) for a general class of critical lattice models, starting from a single initial particle at the origin. Conditions are given on the random sets and an associated ancestral relation under which, conditional on longterm survival, the rescaled ranges converge weakly to the range of super-Brownian motion as random sets. These hypotheses also give precise asymptotics for the limiting behaviour of the probability of exiting a...
