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作者：Kwasnicki, Mateusz
作者单位：Wroclaw University of Science & Technology
摘要：We prove a non-extinction result for Fleming-Viot-type systems of two particles with dynamics described by an arbitrary symmetric Hunt process under the assumption that the reference measure is finite. Additionally, we describe an invariant measure for the system, we discuss its ergodicity, and we prove that the reference measure is a stationary measure for the embedded Markov chain of positions of the surviving particle at successive branching times.
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作者：Boedihardjo, H.; Geng, X.
作者单位：University of Warwick; University of Melbourne
摘要：We show that the tail probability of the rough line integral f(0)(1) phi(X-t)dY(t), where (X, Y) is a 2D fractional Brownian motion with Hurst parameter H is an element of (1/4, 1/2) and phi is a C-b(infinity)-function satisfying a mild non-degeneracy condition on its derivative, cannot decay faster than a gamma-Weibull tail with any exponent gamma > 2H + 1. In particular, this produces a simple class of examples of differential equations driven by fBM, whose solutions fail to have Gaussian ta...
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作者：Huang, Jiaoyang; Mcswiggen, Colin
作者单位：University of Pennsylvania; New York University
摘要：This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature implies a large deviations principle for the hydrodynamic limit of radial Dunkl processes. Using this fact, we prove a variational formula for the large-N asymptotics of generalized Bessel functions, as well as a large deviations principle for the more gener...
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作者：Bazaes, Rodrigo; Lammers, Isabel; Mukherjee, Chiranjib
作者单位：University of Munster
摘要：We construct and study properties of an infinite dimensional analog of Kahane's theory of Gaussian multiplicative chaos (Kahane in Ann Sci Math Quebec 9(2):105-150, 1985). Namely, if H-T (omega) is a random field defined w.r.t. space-time white noise (B) over dot and integrated w.r.t. Brownian paths in d >= 3, we consider the renormalized exponential mu(gamma),T, weighted w.r.t. the Wiener measure P-0(d omega). We construct the almost sure limit mu(gamma) = lim(T ->) (infinity) (mu gamma,T) in...
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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...
