-
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...
-
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...
-
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 ...
-
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...
-
作者：Han, Yi
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Given An:=1n(a(ij)) an nxn symmetric random matrix, with elements above the diagonal given by i.i.d. random variables having mean zero and unit variance. It is known that when limx ->infinity x(4)P(|a(ij)|>x)=0, then fluctuation of the largest eigenvalue of An follows a Tracy-Widom distribution. When the law of aij is regularly varying with index alpha is an element of(0,4), then the largest eigenvalue has a Fr & eacute;chet distribution. An intermediate regime is recently uncovered in Diaconu...
-
作者：Fan, Zhou; Wu, Yihong
作者单位：Yale University
摘要：We study a variant of the Sherrington-Kirkpatrick (S-K) spin glass model with external field, where the random symmetric couplings matrix does not consist of i.i.d. entries but is instead orthogonally invariant in law. For sufficiently high temperature, we prove a replica-symmetric formula for the first-order limit of the model free energy. Our analysis is an adaptation of a conditional second-moment-method argument previously introduced by Bolthausen for studying the high-temperature regime o...
-
作者：Dembin, Barbara; Garban, Christophe
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Institut Universitaire de France
摘要：We consider the standard first passage percolation model on Z(d) with a distribution G taking two values 0 < a < b. We study the maximal flow through the cylinder [0, n](d-1) x [0, hn] between its top and bottom as well as its associated minimal surface(s). We prove that the variance of the maximal flow is superconcentrated, i.e. in O( n(d-1) /log n), for h >= h(0) (for a large enough constant h(0) = h(0)(a, b)). Equivalently, we obtain that the ground state energy of a disordered Ising ferrom...
-
作者：Chak, Martin
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：Given global Lipschitz continuity and differentiability of high enough order on the coefficients in It & ocirc;'s equation, differentiability of associated semigroups, existence of twice differentiable solutions to Kolmogorov equations and weak convergence rates of order one for numerical approximations are known. In this work and against the counterexamples of Hairer et al. (Ann Probab 43(2):468-527, https://doi.org/10.1214/13-AOP838, 2015), the drift and diffusion coefficients having Lipschi...
-
作者：Hong, Guixiang; Ricard, Eric
作者单位：Harbin Institute of Technology; Universite de Caen Normandie; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative L-p-martingales when 1 <= p < 2. The same happens to ergodic averages. The proof consists of some sharp estimates of the distributional function of a sequence of matrices and some non standard transference techniques, which might admit further applications.
-
作者：Cao, Shiping; Qiu, Hua
作者单位：University of Washington; University of Washington Seattle; Nanjing University
摘要：We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the 1/k grids. The intersection of two cells can be a line segment of irrational length, and the non-diagonal assumption is dropped in this recurrent setting.
