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作者：Butori, Federico; Flandoli, Franco; Luongo, Eliseo; Tahraoui, Yassine
作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld
摘要：In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly converge to the solutions of deterministic equations with a diffusion term. In the background of these stochastic models, we introduce stochastic Vlasov equations which give additional information on the fluctuations and oscillations of solutions: we prove co...
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作者：Hong, Wei; Li, Shihu; Liu, Wei
作者单位：Jiangsu Normal University
摘要：In this paper, we provide a general framework for investigating McKean-Vlasov stochastic partial differential equations. We first show the existence of weak solutions by combining the localizing approximation, Faedo-Galerkin technique, compactness method and the Jakubowski version of the Skorokhod representation theorem. Then under certain locally monotone condition we further investigate the existence and uniqueness of (probabilistically) strong solutions. The applications of the main results...
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作者：Lehmkuehler, Matthis; Qian, Wei; Werner, Wendelin
作者单位：University of Basel; University of Hong Kong; University of Cambridge
摘要：The critical two-dimensional Brownian loop-soup is an infinite collection of non-interacting Brownian loops in a planar domain that possesses some combinatorial features related to the notion of indistinguishability of bosons. The properly renormalized occupation time field of this collection of loops is known to be distributed like the properly defined square of a Gaussian free field. In the present paper, we study how much information these fields provide about the loop-soup. Among other thi...
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作者：Husson, Jonathan; Ko, Justin
作者单位：University of Michigan System; University of Michigan; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We consider the asymptotics of rank k spherical integrals when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = o(N)$$\end{document}. We prove that the sublinear rank spherical integrals are approximately the products of rank 1 spherical integrals. Our formulas extend the results for rank k spherical integrals p...
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作者：Fang, Xiao; Liu, Song-Hao; Shao, Qi-Man; Zhao, Yi-Kun
作者单位：Chinese University of Hong Kong; Dalian University of Technology; Southern University of Science & Technology; Southern University of Science & Technology
摘要：The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has remained an open problem. In this paper, we establish the CLT. As a result of our proof, we also derive a convergence rate for the CLT, an explicit formula for the asymptotic variance, and the CLT for general subgraph counts. To establish our main result, we develop Stein's method for the normal approximation of gener...
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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
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作者：Dimitrov, Evgeni; Yang, Zongrui
作者单位：University of Southern California; Columbia University
摘要：We construct a one-parameter family of infinite line ensembles on [0,infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0, \infty )$$\end{document} that are natural half-space analogues of the Airy line ensemble. Away from the origin these ensembles are locally described by avoiding Brownian bridges, and nea...
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作者：Radhakrishnan, Ritvik Ramanan; Tassion, Vincent
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We discuss a general method to obtain quantitative improvements of correlation inequalities and apply it to arm estimates for Bernoulli bond percolation on 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}. Our first result is that the two-arm exponent is strictly larger than twice...
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作者：Jorritsma, Joost; Komjathy, Julia; Mitsche, Dieter
作者单位：University of Oxford; Delft University of Technology; Pontificia Universidad Catolica de Chile
摘要：We study cluster sizes in supercritical d-dimensional inhomogeneous percolation models with long-range edges -such as long-range percolation- and/or heavy-tailed degree distributions -such as geometric inhomogeneous random graphs and the age-dependent random connection model. Our focus is on large deviations of the size of the largest cluster in the graph restricted to a finite box as its volume tends to infinity. Compared to nearest neighbor Bernoulli bond percolation on Zd\documentclass[12pt...
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作者：De Vecchi, Francesco; Fresta, Luca; Gordina, Maria; Gubinelli, Massimiliano
作者单位：University of Pavia; Roma Tre University; University of Connecticut; University of Oxford
摘要：We introduce a theory of non-commutative L-p spaces suitable for non-commutative probability in a non-tracial setting and use it to develop stochastic analysis of Grassmann-valued processes, including martingale inequalities, stochastic integrals with respect to Ito-Grassmann processes, Girsanov's formula and a weak formulation of Grassmann SDEs. We apply this new setting to the construction of several unbounded random variables including a Grassmann analog of the Phi(2)(4) Euclidean QFT in a ...
