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作者：Ang, Morris; Yu, Pu
作者单位：University of California System; University of California San Diego; New York University
摘要：Whole-plane Schramm-Loewner evolution (SLE kappa) is a random fractal curve betweentwo points on the Riemann sphere. Zhan established for kappa <= 4 that whole-plane SLE kappa isreversible, meaning invariant in law under conformal automorphisms swapping itsendpoints. Miller and Sheffield extended this to kappa <= 8. We prove whole-plane SLE kappa is reversible for kappa>8, resolving the final case and answering a conjecture of Viklundand Wang. Our argument depends on a novel mating-of-trees th...
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作者：Grazieschi, P.; Matetski, K.; Weber, H.
作者单位：University of Bath; Michigan State University; University of Munster
摘要：We consider multiple stochastic integrals with respect to c & agrave;dl & agrave;g martingales, which approximate a cylindrical Wiener process. We define a chaos expansion, analogous to the case of multiple Wiener stochastic integrals, for these integrals and use it to show moment bounds. Key tools include an iteration of the Burkholder-Davis-Gundy inequality and a multi-scale decomposition similar to the one developed in Hairer and Quastel (Forum Math Pi 6:e3, 2018). Our method can be combine...
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作者：Berger, Quentin; Legrand, Alexandre
作者单位：Sorbonne Universite; Universite Paris Cite; Universite PSL; Ecole Normale Superieure (ENS); Institut Universitaire de France; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The Poland-Scheragamodel, introduced in the 1970s, is a reference model to describe the denaturation transition of DNA. More recently, it has been generalized in order to allow for asymmetry in the strands lengths and in the formation of loops: the mathematical representation is based on a bivariate renewal process, that describes the pairs of bases that bond together. Here, we consider a disordered version of the model, in which the two strands interact via a potential ss V ( . i, . j) + h wh...
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作者：Li, Songzi; Li, Xiang-Dong
作者单位：Renmin University of China; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
摘要：We prove the Perelman type W-entropy formula for the geodesic flow on the L-2-Wasserstein space over a complete Riemannian manifold equipped with Otto's infinite dimensional Riemannian metric. To better understand the similarity between the W-entropy formula for the geodesic flow on the Wasserstein space and the W-entropy formula for the heat flow of the Witten Laplacian on the underlying manifold, we introduce the Langevin deformation of flows on the Wasserstein space over a Riemannian manifo...
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作者：Henard, Olivier; Maurel-Segala, Edouard; Singh, Arvind
作者单位：Universite Paris Saclay; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider the local limit of uniformly distributed directed animals with size n on the square lattice viewed from the root. Two constructions of the resulting uniform infinite directed animal are given: one as a heap of dominoes, constructed by letting gravity act on a right-continuous random walk, and one as a Markov process, obtained by slicing the animal horizontally. We look at geometric properties of this local limit and establish, in particular, that it consists of a single vertex at i...
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作者：Liu, Dang-Zheng; Zhang, Lu
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：Consider a random matrix of size N as an additive deformation of the complex Ginibre ensemble under a deterministic matrix X0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_0$$\end{document} with a finite rank, independent of N. When some eigenvalues of X0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepac...
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作者：Conforti, Giovanni
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We investigate the quadratic Schrodinger bridge problem, a.k.a. Entropic Optimal Transport problem, and obtain weak semiconvexity and semiconcavity bounds on Schrodinger potentials under mild assumptions on the marginals that are substantially weaker than log-concavity. We deduce from these estimates that Schrodinger bridges satisfy a logarithmic Sobolev inequality on the product space. Our proof strategy is based on a second order analysis of coupling by reflection on the characteristics of t...
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作者：Cercle, Baptiste
作者单位：Universite Paris Saclay
摘要：Toda conformal field theories (CFTs) form a family of 2d CFTs indexed by semisimple and complex Lie algebras. They are natural generalizations of the Liouville CFT in that they enjoy an enhanced level of symmetry encoded by W-algebras. These theories can be rigorously defined using a probabilistic framework that involves the consideration of correlated Gaussian Multiplicative Chaos measures. This document provides a first step towards the computation of a class of three-point correlation funct...
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作者：Bogdan, Krzysztof; Komorowski, Tomasz; Marino, Lorenzo
作者单位：Wroclaw University of Science & Technology; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Institut Polytechnique de Paris; ENSTA Paris
摘要：We consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-killing condition at the interface. Both the coefficient describing the probability of killing and the scattering kernel degenerate. We prove that the long-time, large-space limit is the unique solution of a version of the fractional in space heat equation that corresponds to the Kolmogorov equation for a symmetric stable process, which is reflected, or transmitted while crossing the interface ...
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作者：Lammers, Piet; Ott, Sebastien
作者单位：Universite Paris Saclay; University of Fribourg
摘要：The solid-on-solid model is a model of height functions, introduced to study the interface separating the + and - phase in the Ising model. The planar solid-on-solid model thus corresponds to the three-dimensional Ising model. Delocalisation of this model at high temperature and at zero slope was first derived by Frohlich and Spencer, in parallel to proving the Berezinskii-Kosterlitz-Thouless phase transition. The first main result of this article consists of a simple, alternative proof of del...
