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作者：Garcia, Ernesto; Lessa, Pablo
作者单位：Universidad de la Republica, Uruguay
摘要：We prove that the harmonic measures of certain finite range random walks on Fuchsian Schottky groups, have dimension strictly smaller than the Hausdorff dimension of the corresponding limit set.
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作者：Barany, Balazs; Rams, Michal
作者单位：Budapest University of Technology & Economics; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than 1 at every point is absolutely continuous with H & ouml;lder continuous density almost surely. In particular, if the similarity dimension is greater than 1 then the random self-similar set on the line contains an interior point almost surely.
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作者：Sly, Allan; Sohn, Youngtak
作者单位：Princeton University; Massachusetts Institute of Technology (MIT)
摘要：The local behavior of typical solutions of random constraint satisfaction problems (CSP) describes many important phenomena including clustering thresholds, decay of correlations, and the behavior of message passing algorithms. When the constraint density is low, studying the planted model is a powerful technique for determining this local behavior which in many examples has a simple Markovian structure. The work of Coja-Oghlan, Kapetanopoulos, Muller (Comb Prob Comput 29:346-422, 2020) showed...
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作者：Su, Yiming; Zhang, Deng
作者单位：Hangzhou Normal University; Shanghai Jiao Tong University
摘要：We study the bubbling phenomena for focusing mass-critical nonlinear Schr & ouml;dinger equations, driven by linear multiplicative noise in the sense of controlled rough paths. In both dimensions one and two, we give a pathwise construction of stochastic multi-bubble blow-up solutions, which concentrate at finitely many distinct points, and behave asymptotically like a sum of pseudo-conformal blow-up solutions. In particular, this provides the first examples of mass quantization phenomenon in ...
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作者：Cai, Zhenhao; Procaccia, Eviatar B.; Zhang, Yuan
作者单位：Weizmann Institute of Science; Technion Israel Institute of Technology; Renmin University of China; Renmin University of China
摘要：We study the harmonic measure (i.e. the limit of the hitting distribution of a simple random walk starting from a distant point) on three canonical two-dimensional lattices: the square lattice Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}<^>2$$\end{document}, the triangular lattice T\documentclass[1...
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作者：Fredes, Luis; Sepulveda, Avelio
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
摘要：The (non-spanning) tree decorated quadrangulation is a random pair consisting of a quadrangulation and a subtree chosen uniformly over the set of pairs with a prescribed size. In this paper, we study the tree decorated quadrangulation in the critical regime: when the number f of faces of the map is proportional to the square of the size of the tree. We show that with high probability in this regime, the diameter of the tree lies between o(f(1/4)) and f(1/4)/log(alpha)(f), for all alpha > 1. Th...
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作者：Gabriel, Simon; Rosati, Tommaso; Zygouras, Nikos
作者单位：University of Munster; University of Warwick
摘要：This work considers the two-dimensional Allen-Cahn equation partial derivative tu=12 Delta u+mu-u3,u(0,x)=eta(x),for all(t,x)is an element of[0,infinity)xR2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \partial _t u = \frac{1}{2}\Delta u + \mathfrak {m}\, u -u<^>3, \quad u(0,x)= \eta (x), \qquad ...
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作者：Bertoin, Jean; Mallein, Bastien
作者单位：University of Zurich; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier
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...
