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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...
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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...
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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...
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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.
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作者：Baraud, Yannick
作者单位：University of Luxembourg
摘要：In the Bayes paradigm, given a loss function and an n-sample, we present the construction of a new type of posterior distribution, that extends the classical Bayes one. The loss functions we have in mind are either those derived from the total variation and Hellinger distances or some L-j-ones for j > 1. We prove that, with a probability close to one, this new posterior distribution concentrates its mass in a neighbourhood (for the chosen loss function) of the law of the data, provided that th...
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作者：Brazitikos, Silouanos; Giannopoulos, Apostolos; Pafis, Minas
作者单位：National & Kapodistrian University of Athens
摘要：Given a probability measure mu on R-n, Tukey's half-space depth is defined for any x is an element of R-n by phi(mu)(x) = inf{mu (H) : H is an element of H(x)}, where H(x) is the set of all half-spaces H of R-n containing x. We show that if mu is a non-degenerate log-concave probability measure on R-n thene(-c1n) <= integral (n)(R)phi mu (x) d mu (x) <= e(mu)(-c2n/L2)where L-mu is the isotropic constant of mu and c(1), c(2) > 0 are absolute constants. The proofs combine large deviations techni...
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作者：Mikulincer, Dan; Shenfeld, Yair
作者单位：Massachusetts Institute of Technology (MIT); Brown University
摘要：Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however, is a non-trivial task and, so far, relies mostly on the theory of optimal transport. In this work, we take advantage of the infinite-dimensional nature of the Gaussian measure and construct a new transport map, based on the F & ouml;llmer process, which pushes forward the Wiener measure onto probability measures on...
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作者：Banerjee, Sayan; Bhamidi, Shankar; Huang, Xiangying
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Co-evolving network models, wherein dynamics such as randomwalks on the network influence the evolution of the network structure, which in turn influences the dynamics, are of interest in a range of domains. While much of the literature in this area is currently supported by numerics, providing evidence for fascinating conjectures and phase transitions, proving rigorous results has been quite challenging. We propose a general class of co-evolving tree network models driven by local exploration...
