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作者：Feng, Yuyang
作者单位：University of Chicago
摘要：We consider infinite random planar maps decorated by the critical Fortuin-Kasteleyn model with parameter q > 4. The paper demonstrates that when appropriately rescaled, these maps converge in law to the infinite continuum random tree as pointed metric-measure spaces, that is, with respect to the local Gromov-Hausdorff-Prokhorov topology. Furthermore, we also show that these maps do not admit any Fortuin-Kasteleyn loops with a macroscopic graph distance diameter. Our proof is based on Scott She...
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作者：Janson, Svante
作者单位：Uppsala University
摘要：Uncover the vertices of a given graph, deterministic or random, in uniformly random order; we consider both a discrete-time and a continuous-time version. We study the evolution of the number of visible edges, and show convergence after normalization to a Gaussian process. This problem was studied by Hackl, Panholzer, and Wagner for the case when the graph is a uniformly random labelled tree; we generalize their result to more general graphs, including both other classes of random and non-rand...
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作者：Parraud, Felix; Schnelli, Kevin
作者单位：Royal Institute of Technology
摘要：In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of polynomials evaluated in those matrices. We prove an asymptotic expansion in the inverse of the matrix dimension to any order. Out of this result we deduce new formulas for map enumerations and the microstates free entropy. Our approach is based on the interpolatio...
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作者：Forsstrom, Malin P.; Gantert, Nina; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of {0,1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{0,1\}$$\end{document}-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our main focus ...
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作者：Dembo, Amir; Subag, Eliran
作者单位：Stanford University; Weizmann Institute of Science
摘要：We study the law of a random field fN(sigma) evaluated at a random sample from the Gibbs measure associated to a Gaussian field HN(sigma) . In the high-temperature regime, we show that bounds on the probability that fN(sigma)is an element of A for sigma randomly sampled from the Gibbs measure can be deduced from similar bounds for deterministic sigma under the conditional Gaussian law given that HN(sigma)/N=E for E close to the derivative F '(beta) of the free energy (which is the typical valu...
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作者：Fevrier, Maxime; Nica, Alexandru; Szpojankowski, Kamil
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of Waterloo; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Warsaw University of Technology
摘要：We study the problem of free denoising. For free selfadjoint random variables a, b, where we interpret a as a signal and b as noise, we find E(a|a+b)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ E (a \, | \, a+b)$$\end{document}. To that end, we study a probability measure mu a,a+b(ov)\documentclass[12pt]{minima...
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作者：Gu, Chenlin; Su, Zhonggen; Xu, Ruizhe
作者单位：Tsinghua University; Zhejiang University
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作者：Bertoin, Jean; Mallein, Bastien
作者单位：University of Zurich; Communaute d'universites et etablissements de Toulouse (Comue); Universite de Toulouse (EPE); Institut National des Sciences Appliquees de Toulouse
摘要：Reinforced Galton-Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forbearers can be repeated randomly by descendants. More specifically, the evolution depends on the empirical offspring distribution of each individual along its ancestral lineage. We are interested here in asymptotic properties of the empirical distributions observed in the population, such as concentration, evanescence and persistence. For ...
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作者：Roeckner, Michael; Zhao, Guohuan
作者单位：University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This paper is a continuation of (R & ouml;ckner and Zhao, Bernoulli 29(1), 821 757-784 (2023)). Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the strong solvability of time-inhomogeneous stochastic differential equations with drift coefficients in critical Lebesgue spaces, which gives an affirmative answer to a longstanding open problem. As an application, we also prove a regularity criterion for solutions of a stochastic system proposed b...
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作者：Huang, Han; Tikhomirov, Konstantin
作者单位：University of Missouri System; University of Missouri Columbia; Carnegie Mellon University
摘要：Given a positive integer n, an unlabeled graph G on n vertices, and a vertex v of G, let N-G(v) be the subgraph of G induced by vertices of G of distance at most one from v. We show that there are universal constants C, c > 0 with the following property. Let the sequence (p(n))(n=1)(8) satisfy n(-1/2) log(n)(C) <= pn <= c. For each n, let Gamma(n) be an unlabeled G(n, p(n)) Erdos-Renyi graph. Then with probability 1 - o(n)(1), any unlabeled graph (Gamma) over tilde (n) on n vertices with {N (G...
