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作者：Ren, Panpan; Wang, Feng-Yu
作者单位：Tianjin University; City University of Hong Kong
摘要：By developing a new technique called the bi-coupling argument, we estimate the relative entropy between different diffusion processes in terms of the distances of initial distributions and drift-diffusion coefficients. As an application, the entropy-cost inequality is established for McKean-Vlasov SDEs with spatial-distribution dependent noise, which is open for a long time and has potential applications in optimal transport, information theory and mean field particle systems.
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作者：Chiarini, Alberto; Pasqui, Emanuele
摘要：We study the discrete Gaussian free field (harmonic crystal) on Z(d) , d >= 3 , with uniformly elliptic and bounded random conductances sampled according to a sufficiently mixing environment measure. We consider the hard wall event that the field is non-negative on the discrete blow-up of a bounded regular domain V subset of R-d , and establish a quenched large deviation asymptotic for its probability. The asymptotic rate is characterized by the essential supremum of the on-site variances and ...
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作者：Abdalla, Pedro; Mendelson, Shahar
作者单位：University of California Irvine; University of California System; University of California Irvine; ETH Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We construct an estimator for covariance matrices of unknown, centred random vectors X, with the given data consisting of N independent measurements X1,& mldr;,XN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_1,\ldots ,X_N$$\end{document} of X and the wanted confidence level. We show under minimal assumptions on...
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作者：Groathouse, Sean; Rassoul-Agha, Firas; Seppalainen, Timo; Sorensen, Evan
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison; Columbia University
摘要：We give an explicit description of a family of jointly invariant measures of the KPZ equation singled out by asymptotic slope conditions. These are couplings of Brownian motions with drift, and can be extended to a cadlag process indexed by all real drift parameters. We name this process the KPZ horizon (KPZH). As a corollary, we resolve a recent conjecture by showing the existence of a random, countably infinite dense set of drift values at which the Busemann process of the KPZ equation is di...
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作者：He, Jimmy
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six vertex model in a half space, from which we obtain results on the asymmetric simple exclusion process, as well as for the beta polymer through a fusion procedure which may be of independent interest. As an application, we establish a distributional identity between the absorption time in a type B an...
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作者：Feldheim, Naomi; Haimi, Antti; Koliander, Gunther; Romero, Jose Luis
作者单位：Bar Ilan University; Austrian Academy of Sciences; University of Vienna
摘要：We study zero sets of twisted stationary Gaussian random functions on the complex plane, i.e., Gaussian random functions that are stochastically invariant under the action of the Weyl-Heisenberg group. This model includes translation-invariant Gaussian entire functions (GEFs), and also many other non-analytic examples, in which case winding numbers around zeros can be either positive or negative. We investigate zero statistics both when zeros are weighted with their winding numbers (charged ze...
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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：Kim, Yujin H.; Zeitouni, Ofer
作者单位：New York University; Weizmann Institute of Science; New York University
摘要：We study the shape of the outer envelope of a branching Brownian motion (BBM) 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}, d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage...
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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...
