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作者：Jego, Antoine; Lupu, Titus; Qian, Wei
作者单位：Universite PSL; Universite Paris-Dauphine; Sorbonne Universite
摘要：We show that the occupation measure of planar Brownian motion exhibits a constant height gap of across its outer boundary. This property bears similarities with the celebrated results of Schramm-Sheffield (Schramm and Sheffield in Probab Theory Related Fields 157(1-2):47-80, 2013) and Miller-Sheffield (Miller J, Sheffield S in CLE(4) and the Gaussian free field. In preparation) concerning the height gap of 5/pi the Gaussian free field across SLE4/CLE4 curves. Heuristically, our result can also...
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作者：Duminil-Copin, Hugo; Panis, Romain
作者单位：Universite Paris Saclay; University of Geneva; Centre National de la Recherche Scientifique (CNRS); Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon
摘要：This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions d > 6. We obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. In a companion paper, we apply a similar analysis to the study of the weakly self-avoiding walk model in dimensions d > 4 [Duminil-Copin and Panis, arXiv:2410.03649, (2024)].
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Ji, Hong Chang
作者单位：Institute of Science & Technology - Austria; University of Arizona; University of Wisconsin System; University of Wisconsin Madison
摘要：For general large non-Hermitian random matrices X and deterministic normal deformations A, we prove that the local eigenvalue statistics of A+X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A+X$$\end{document} close to the critical edge points of its spectrum are universal. This concludes the proof of the third an...
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作者：Hazra, Rajat Subhra; den Hollander, Frank; Parvaneh, Azadeh
作者单位：Leiden University - Excl LUMC; Leiden University
摘要：Let Gn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_n$$\end{document} be an undirected finite graph on n is an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{...
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作者：Hermon, Jonathan; Huang, Xiangying; Pedrotti, Francesco; Salez, Justin
作者单位：University of British Columbia; University of North Carolina; University of North Carolina Chapel Hill; Swiss Federal Institutes of Technology Domain; ETH Zurich; Universite PSL; Universite Paris-Dauphine
摘要：Motivated by the Asymptotic Equipartition Property and its recently discovered role in the cutoff phenomenon, we initiate the systematic study of varentropy on discrete groups. Our main result is an approximate tensorization inequality which asserts that the varentropy of any conjugacy-invariant random walk is, up to a universal multiplicative constant, at most that of the free Abelian random walk with the same jump rates. In particular, it is always bounded by the number d of generators, unif...
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作者：Galeati, Lucio; Grotto, Francesco; Maurelli, Mario
作者单位：University of L'Aquila; University of Pisa
摘要：We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and Holder regular in space (rough Kraichnan's model), a well-established synthetic model of passive scalar turbulence. By studying the evolution of negative Sobolev norms, we show an anomalous regularization effect induced by the dynamics: distributional initial conditions immediately become functions of positive Sobolev regularity.
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作者：Faggionato, Alessandra
作者单位：Sapienza University Rome
摘要：Mott's variable range hopping (v.r.h.) is the phonon-induced hopping of electrons in disordered solids (such as doped semiconductors) within the regime of strong Anderson localization. It was introduced by N. Mott to explain the anomalous low temperature conductivity decay in dimension d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{...
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作者：Bolbotowski, Karol; Bouchitte, Guy
作者单位：University of Warsaw
摘要：Based on a new Kantorovich-Rubinstein duality principle for the Hessian that was recently established by the two authors, we extend the Rio inequality to any dimension d >= 1 with an optimal constant. Similarly, we propose an optimal upper bound for the ratio of Zolotarev distance Z2(mu,nu) to Wasserstein distance W2(mu,nu) when mu,nu is an element of P2(Rd) are centred probabilities with prescribed variances.
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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...
