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作者：Koike, Yuta
作者单位：University of Tokyo; Japan Science & Technology Agency (JST)
摘要：The recent seminal work of Chernozhukov, Chetverikov and Kato has shown that bootstrap approximation for the maximum of a sum of independent random vectors is justified even when the dimension is much larger than the sample size. In this context, numerical experiments suggest that third-moment matching bootstrap approximations would outperform normal approximation even without studentization, but the existing theoretical results cannot explain this phenomenon. In this paper, we develop an asym...
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作者：Muirhead, Stephen; Wigman, Igor
作者单位：University of Melbourne; University of London; King's College London; Monash University
摘要：We establish the existence and uniqueness of a well-concentrated giant component in the supercritical excursion sets of three important ensembles of spherical Gaussian random fields: Kostlan's ensemble, band-limited ensembles, and the random spherical harmonics. Our main results prescribe quantitative bounds for the volume fluctuations of the giant that are essentially optimal for non-monochromatic ensembles, and suboptimal but still strong for monochromatic ensembles. Our results support the ...
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作者：Garban, Christophe; Vargas, Vincent
作者单位：Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Universitaire de France; University of Geneva; University of Geneva
摘要：In this paper, we initiate the harmonic analysis of Gaussian multiplicative chaos (GMC) on the circle, i.e. the study of its Fourier coefficients. In particular, we show that almost surely GMC is a so-called Rajchman measure which means that its Fourier coefficients converge to 0 when the frequency goes to infinity. We supplement this result with a convergence in law result for the rescaled Fourier coefficients.
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作者：Grube, Sebastian
作者单位：University of Bielefeld
摘要：While the nondegenerate case is well known, there are only few results on the existence of strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type in the degenerate case. We consider a broad class of degenerate nonlinear Fokker-Planck(-Kolmogorov) equations with coefficients of Nemytskii-type. This includes, in particular, the classical porous medium equation perturbed by a first-order term with initial datum in a subset of probability densities, which is dense with respect ...
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作者：Clark, J. M. C.; Crisan, Dan
作者单位：Imperial College London
摘要：This paper studies the identification of an 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}-valued diffusion X when a running function of it, say h(Xt)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsb...
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作者：Gorin, Vadim; Kenyon, Richard
作者单位：University of California System; University of California Berkeley; Yale University
摘要：We study limit shapes in two equivalent models: the six-vertex model in the c -> 0 limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-Lagrange equation for the limit shape and show how to solve it for a class of rectilinear polygonal domains. Its solutions are given by piecewise-algebraic functions with lines of discontinuities.
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作者：Can, Van Hao; Kubota, Naoki; Nakajima, Shuta
作者单位：Vietnam Academy of Science & Technology (VAST); Nihon University; Keio University
摘要：In this paper, we study the upper tail large deviation for the one-dimensional frog model. In this model, sleeping and active frogs are assigned to sites of Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}$$\end{document}. While sleeping frogs do not move, the active ones move as independent simple rand...
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作者：Schmid, Dominik; Yang, Zongrui
作者单位：University of Augsburg; Columbia University
摘要：We consider the stationary measure of the open asymmetric simple exclusion process (ASEP) with light particles. We prove several results on the asymptotic locations of the light particles under the stationary measure. Moreover, in the fan region of the high and low density phases, we study the mixing times for open ASEP with light particles. Our approach involves the matrix product ansatz, Askey-Wilson signed measures, moderate deviation results for second class particles, as well as various c...
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作者：Deuschel, Jean-Dominique; Kumagai, Takashi; Slowik, Martin
作者单位：Technical University of Berlin; Waseda University; University of Mannheim
摘要：In this paper we consider a time-continuous random walk in Z(d) in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these random conductances are stationary and ergodic and, moreover, that they are bounded from below but unbounded from above with finite first moment. We derive sharp on-diagonal estimates for the annealed first and second discrete space derivative of the heat kernel which then yield local limit theorems for the corresponding kernels...
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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...
