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作者：Marahrens, Daniel; Otto, Felix
作者单位：Max Planck Society
摘要：We consider a random, uniformly elliptic coefficient field on the -dimensional integer lattice . We are interested in the spatial decay of the quenched elliptic Green function . Next to stationarity, we assume that the spatial correlation of the coefficient field decays sufficiently fast to the effect that a logarithmic Sobolev inequality holds for the ensemble . We prove that all stochastic moments of the first and second mixed derivatives of the Green function, that is, and , have the same d...
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作者：Gorin, Vadim; Shkolnikov, Mykhaylo
作者单位：Massachusetts Institute of Technology (MIT); Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; University of California System; University of California Berkeley
摘要：We introduce multilevel versions of Dyson Brownian motions of arbitrary parameter , generalizing the interlacing reflected Brownian motions of Warren for . Such processes unify corners processes and Dyson Brownian motions in a single object. Our approach is based on the approximation by certain multilevel discrete Markov chains of independent interest, which are defined by means of Jack symmetric polynomials. In particular, this approach allows to show that the levels in a multilevel Dyson Bro...
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作者：Mossel, Elchanan; Neeman, Joe; Sly, Allan
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Australian National University
摘要：The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer science. In its simplest form, the planted partition model is a model for random graphs on nodes with two equal-sized clusters, with an between-class edge probability of and a within-class edge probability of . Although most of the literature on this model has focused on the case of increasing degrees (...
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作者：Kiss, Demeter
作者单位：University of Cambridge; Tohoku University
摘要：Aldous (Math Proc Camb Philos Soc 128:465-477, 2000) introduced a modification of the bond percolation process on the binary tree where clusters stop growing (freeze) as soon as they become infinite. We investigate the site version of this process on the triangular lattice where clusters freeze as soon as they reach diameter at least for some parameter . We show, informally speaking, that in the limit , the clusters only freeze in the critical window of site percolation on the triangular latti...
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作者：Daskalakis, Constantinos; Papadimitriou, Christos
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：For all , we show that the set of Poisson Binomial distributions on variables admits a proper -cover in total variation distance of size , which can also be computed in polynomial time. We discuss the implications of our construction for approximation algorithms and the computation of approximate Nash equilibria in anonymous games.
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作者：Zhan, Dapeng
作者单位：Michigan State University
摘要：The main result of this paper is that, for , whole-plane SLE satisfies reversibility, which means that the time-reversal of a whole-plane SLE trace is still a whole-plane SLE trace. In addition, we find that the time-reversal of a radial SLE trace for is a disc SLE trace with a marked boundary point. The main tool used in this paper is a stochastic coupling technique, which is used to couple two whole-plane SLE traces so that they overlap. Another tool used is the Feynman-Kac formula, which is...
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作者：Brzezniak, Z.; Cerrai, S.; Freidlin, M.
作者单位：University of York - UK; University System of Maryland; University of Maryland College Park
摘要：We are dealing with the Navier-Stokes equation in a bounded regular domain of , perturbed by an additive Gaussian noise , which is white in time and colored in space. We assume that the correlation radius of the noise gets smaller and smaller as , so that the noise converges to the white noise in space and time. For every we introduce the large deviation action functional and the corresponding quasi-potential and, by using arguments from relaxation and -convergence we show that converges to , ...
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作者：Cai, Tony; Ma, Zongming; Wu, Yihong
作者单位：University of Pennsylvania; University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper considers a sparse spiked covariance matrix model in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of convergence for estimating the spiked covariance matrix under the spectral norm is established, which requires significantly different techniques from those for estimating other structured covariance matrices such as bandable or sparse covariance matrices. We...
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作者：Hammond, Alan
作者单位：University of Oxford
摘要：We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists such that, for any , the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree almost surely contains an infinite cycle consists of a semi-infinite interval. The critical point at the left-hand end of this interval is at least and at most .
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作者：Debussche, A.; Vovelle, J.
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the invariant measure. Also, since this invariant measure is supported by for some small, we are led to generalize to the stochastic case the theory of solutions developed by Ch...
