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作者：Mariani, Mauro; Pardoux, Etienne; Velleret, Aurelien
作者单位：HSE University (National Research University Higher School of Economics); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual reproduction mode in preventing the accumulation of deleterious mutations through natural selection alone. The main considered model is non-classical, as it is a stochastic diffusion evolving on an irregular set of infinite dimension with hard killing on a hyperplane. ...
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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：Berger, Noam; Conache, Diana; Johansson, Anders; Oberg, Anders
作者单位：Technical University of Munich; University of Gavle; Uppsala University
摘要：In this paper we solve two open problems in ergodic theory. We prove first that if a Doeblin function g (a g-function) satisfies lim sup(n ->infinity)var(n)log g / n(-1/2 )<2, then we have a unique Doeblin measure (g-measure). This result indicates a possible phase transition in analogy with the long-range Ising model. Secondly, we provide an example of a Doeblin function with a unique Doeblin measure that is not weakly mixing, which implies that the sequence of iterates of the transfer operat...
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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：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：Barany, Balazs; Kaenmaki, Antti; Rams, Michal
作者单位：Budapest University of Technology & Economics; University of Eastern Finland; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We compute the almost sure Hausdorff dimension of random self-affine sponges 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} without imposing any separation conditions. In this context, randomness arises from the matrices in the defining semigroup, which are random yet the corre...
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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.
