Probability Theory and Related Fields

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• Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise AI翻译
  作者：Hofmanova, Martina; Lange, Theresa; Pappalettera, Umberto
  作者单位：University of Bielefeld
  摘要：We construct Holder continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can be chosen arbitrarily large with high probability. We also prove that there exist infinitely many Holder continuous initial conditions leading to non-uniqueness of solutions to the Cauchy problem associated with the system. Our construction relies on a flow tr...
• Mixing time of random walk on dynamical random cluster AI翻译
  作者：Lelli, Andrea; Stauffer, Alexandre
  作者单位：University of Bath; University of London; King's College London
  摘要：We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} between open and closed, following a Glauber dynamics for the random c...
• Half-space depth of log-concave probability measures AI翻译
  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...
• On questions of uniqueness for the vacant set of Wiener sausages and Brownian interlacements AI翻译
  作者：Mu, Yingxin; Sapozhnikov, Artem
  作者单位：Leipzig University
  摘要：We consider connectivity properties of the vacant set of (random) ensembles of Wiener sausages in Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}<^>d$$\end{document} in the transient dimensions d >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepa...
• Optimal transport methods for combinatorial optimization over two random point sets AI翻译
  作者：Goldman, Michael; Trevisan, Dario
  作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; University of Pisa
  摘要：We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>d$$\end{document} where the edge cost between two points is given by a pth power of their Euclidean distance. This includes...
• The Brownian transport map AI翻译
  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...
• Co-evolving dynamic networks AI翻译
  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...
• The number of critical points of a Gaussian field: finiteness of moments AI翻译
  作者：Gass, Louis; Stecconi, Michele
  作者单位：University of Luxembourg
  摘要：Let f be a Gaussian random field on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>d$$\end{document} and let X be the number of critical points of f contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on f, the random variable X has...
• On the ergodicity of interacting particle systems under number rigidity AI翻译
  作者：Suzuki, Kohei
  作者单位：Durham University
  摘要：In this paper, we provide relations among the following properties: (a) the tail triviality of a probability measure mu on the configuration space Gamma; (b) the finiteness of a suitable L-2-transportation-type distance (d) over bar (Gamma); (c) the irreducibility of local mu-symmetric Dirichlet forms on Gamma. As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction and arising from determinantal/p...
• Phase transition for random walks on graphs with added weighted random matching AI翻译
  作者：Baran, Zsuzsanna; Hermon, Jonathan; Sarkovic, Andela; Sousi, Perla
  作者单位：University of Cambridge; University of British Columbia
  摘要：For a finite graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=(V,E)$$\end{document} let G & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin...