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作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroder, Dominik
作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tra-cial mode, Tr f (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Tr f (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diago...
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作者：Shapira, Assaf
作者单位：Universite Paris Cite
摘要：This paper concerns with the hydrodynamic limit of the Kob-Andersen model, an interacting particle system that has been introduced by physicists in order to explain glassy behavior, and widely studied since. We will see that the density profile evolves in the hydrodynamic limit according to a nondegenerate hydrodynamic equation, and understand how the diffusion coefficient decays as density grows.
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作者：Gravner, Janko; Kolesnik, Brett
作者单位：University of California System; University of California Davis; University of California System; University of California San Diego
摘要：We introduce and study a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap percolation, and percolation in polluted environments. Start with an oriented graph G0 of initially occu-pied edges on n vertices, and iteratively occupy additional (oriented) edges by transitivity, with the constraint that only open edges in a certain random set can ever be occupied. All other edges are closed, creating a set of obsta-cles for the spread of occupied edges. When G0 i...
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作者：Blancas, Airam; Gufler, Stephan; Kliem, Sandra; Tran, Viet chi; Wakolbinger, Anton
作者单位：Instituto Tecnologico Autonomo de Mexico; Goethe University Frankfurt; Leipzig University; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：For a continuous state branching process with two types of individuals which are subject to selection and density dependent competition, we characterize the joint evolution of population size, type configurations and genealogies as the unique strong solution of a system of SDEs. Our construction is achieved in the lookdown framework and provides a synthesis as well as a generalization of cases considered separately in two seminal papers by Donnelly and Kurtz (Ann. Appl. Probab. 9 (1999) 1091-1...
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作者：Wu, Yihong; Xu, Jiaming; Yu, Sophie H.
作者单位：Yale University; Duke University
摘要：We study the problem of detecting the edge correlation between two ran-dom graphs with n unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated; under the alternative, the two graphs are edge-correlated under some latent node correspondence, but have the same marginal distributions as the null. For both Gaussian-weighted complete graphs and dense Erd6s- Renyi graphs (with edge probability n-o(1)), we dete...
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作者：Cerny, Jiri; Drewitz, Alexander; Schmitz, Lars
作者单位：University of Basel; University of Cologne
摘要：We investigate the uniform boundedness of the fronts of the solutions to the randomized Fisher-KPP equation and to its linearization, the parabolic Anderson model. It has been known that for the standard (i.e., deterministic) Fisher-KPP equation, as well as for the special case of a randomized Fisher-KPP equation with so-called ignition type nonlinearity, the transition front is uniformly bounded (in time). Here, we show that this property of having a uniformly bounded transition front fails t...
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作者：Chen, Peng; Shao, Qi-Man; Xu, Lihu
作者单位：Nanjing University of Aeronautics & Astronautics; Southern University of Science & Technology; University of Macau
摘要：We view the classical Lindeberg principle in a Markov process setting to establish a probability approximation framework by the associated Ito's for-mula and Markov operator. As applications, we study the error bounds of the following three approximations: approximating a family of online stochastic gradient descents (SGDs) by a stochastic differential equation (SDE) driven by multiplicative Brownian motion, Euler-Maruyama (EM) discretization for multi-dimensional Ornstein-Uhlenbeck stable pro...
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作者：Bai, Tianyi; Hu, Yueyun
作者单位：New York University; NYU Shanghai
摘要：Let R-n be the range of a critical branching random walk with n particles on Z(d) , which is the set of sites visited by a random walk indexed by a critical Galton- Watson tree conditioned on having exactly n vertices. For d is an element of {3, 4, 5}, we prove that n - (d-2)/(4) cap((d)) (R-n), the renormalized capacity of Rn, converges in law to the capacity of the support of the integrated super-Brownian excursion. The proof relies on a study of the intersection probabilities between the cr...
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作者：Feireisl, Eduard; Cova-medvidova, Maria Luka
作者单位：Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; Johannes Gutenberg University of Mainz
摘要：We propose a stochastic collocation method based on the piecewise con -stant interpolation on the probability space combined with a finite volume method to solve the compressible Navier-Stokes system at the nodal points. We show convergence of numerical solutions to a statistical solution of the Navier-Stokes system on condition that the numerical solutions are bounded in probability. The analysis uses the stochastic compactness method based on the Skorokhod/Jakubowski representation theorem a...
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作者：Glatt-holtz, Nathan; Krometis, Justin; Mondaini, Cecilia
作者单位：Tulane University; Virginia Polytechnic Institute & State University; Virginia Polytechnic Institute & State University; Drexel University
摘要：This work develops a powerful and versatile framework for determin-ing acceptance ratios in Metropolis-Hastings-type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which unify random walk or diffusion-type sampling meth-ods with more complicated extended phase space algorithms based around ideas from Hamiltonian dynamics. Our starting point is an abstract result de-veloped in the generality of measurable state spaces that ad...
