Probability Theory and Related Fields

最新文章

• Local convergence rates for Wasserstein gradient flows and McKean-Vlasov equations with multiple stationary solutions AI翻译
  作者：Monmarche, Pierre; Reygner, Julien
  作者单位：Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
  摘要：Non-linear versions of log-Sobolev inequalities, that link a free energy to its dissipation along the corresponding Wasserstein gradient flow (i.e. corresponds to Polyak-Lojasiewicz inequalities in this context), are known to provide global exponential long-time convergence to the free energy minimizers, and have been shown to hold in various contexts. However they cannot hold when the free energy admits critical points which are not global minimizers, which is for instance the case of the gra...
• A geometric approach to conjugation-invariant random permutations AI翻译
  作者：Dubach, Victor
  作者单位：Uppsala University
  摘要：We propose a new approach to conjugation-invariant random permutations. Namely, we explain how to construct uniform permutations in given conjugacy classes from certain point processes in the plane. This enables the use of geometric tools to study various statistics of such permutations. For their longest decreasing subsequences, we prove universality of the 2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} ...
• Decorrelation transition in the Wigner minor process AI翻译
  作者：Bao, Zhigang; Cipolloni, Giorgio; Erdos, Laszlo; Henheik, Joscha; Kolupaiev, Oleksii
  作者单位：University of Hong Kong; University of Arizona; Institute of Science & Technology - Austria
  摘要：We consider the Wigner minor process, i.e. the eigenvalues of an NxN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\times N$$\end{document} Wigner matrix H(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
• Mixing of fast random walks on dynamic random permutations AI翻译
  作者：Avena, Luca; van der Hofstad, Remco; den Hollander, Frank; Nagy, Oliver
  作者单位：University of Florence; Eindhoven University of Technology; Leiden University; Leiden University - Excl LUMC
  摘要：We analyse the mixing profile of a random walk on a dynamic random permutation, focusing on the regime where the walk evolves much faster than the permutation. Two types of dynamics generated by random transpositions are considered: one allows for coagulation of permutation cycles only, the other allows for both coagulation and fragmentation. We show that for both types, after scaling time by the length of the permutation and letting this length tend to infinity, the total variation distance b...
• Gibbs measures as local equilibrium KMS states for focusing nonlinear Schrödinger equations AI翻译
  作者：Ammari, Zied; Rout, Andrew; Sohinger, Vedran
  作者单位：Universite Marie et Louis Pasteur; Polytechnic University of Milan; University of Warwick
  摘要：In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear Schr & ouml;dinger and Hartree equations on the d-dimensional torus Td\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {T}<^>d$$\end{document} when d=1,2,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepac...
• Global geometry within an SPDE well-posedness problem AI翻译
  作者：Chen, Hongyi; Ouyang, Cheng
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
  摘要：On a closed Riemannian manifold, we construct a family of intrinsic Gaussian noises indexed by a regularity parameter alpha >= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \ge 0$$\end{document} to study the well-posedness of the parabolic Anderson model. We show that with rough initial conditions, the eq...
• The scaling limit of the root component in the Wired Minimal Spanning Forest of the Poisson Weighted Infinite Tree AI翻译
  作者：Angel, Omer; Senizergues, Delphin
  作者单位：University of British Columbia; Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper we prove a scaling limit result for the component of the root in the Wired Minimal Spanning Forest (WMSF) of the Poisson-Weighted Infinite Tree (PWIT), where the latter tree arises as the local weak limit of the Minimal Spanning Tree (MST) on the complete graph endowed with i.i.d. weights on its edges. The limiting object M infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mat...
• Two-dimensional forest fires with boundary ignitions AI翻译
  作者：Van Den Berg, Jacob; Nolin, Pierre
  作者单位：Centrum Wiskunde & Informatica (CWI); City University of Hong Kong
  摘要：In the classical Drossel-Schwabl forest fire process, vertices of a lattice become occupied at rate 1, and they are hit by lightning at some tiny rate zeta > 0, which causes entire connected components to burn. In this paper, we study a variant where fires are coming from the boundary of the forest instead. In particular we prove for every positive zeta (including zeta = infinity) that, for the forest fire process without recoveries on an N x N box in the triangular lattice, where each point o...
• Optimal unimodular matchings AI翻译
  作者：Enriquez, Nathanael; Liu, Mike; Menard, Laurent; Perchet, Vianney
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS)
  摘要：We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the limiting tree. For this purpose, we introduce and study unimodular matchings on weighted unimodular random trees as well as a notion of optimality for these objects. In this context, we prove that, in law, there is a unique optimal unimodular matching for a give...
• Fractal random sets associated with multitype Galton-Watson trees AI翻译
  作者：Calka, Pierre; Demichel, Yann
  作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper, we consider a regular tessellation of the Euclidean plane and the sequence of its geometric scalings by negative powers of a fixed integer. We generate iteratively random sets as the union of adjacent tiles from these rescaled tessellations. We encode this geometric construction into a combinatorial object, namely a multitype Galton-Watson tree. Our main result concerns the geometric properties of the limiting planar set. In particular, we show that both box and Hausdorff dimens...