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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：Li, Xinyi; Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We derive a large deviation principle for the density profile of occupation times of random interlacements at a fixed level in a large box of , . As an application, we analyze the asymptotic behavior of the probability that atypically high values of the density profile insulate a macroscopic body in a large box. As a step in this program, we obtain a similar large deviation principle for the occupation-time measure of Brownian interlacements at a fixed level in a large box of , and we derive a...
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作者：Rakhlin, Alexander; Sridharan, Karthik; Tewari, Ambuj
作者单位：University of Pennsylvania; University of Michigan System; University of Michigan
摘要：We establish necessary and sufficient conditions for a uniform martingale Law of Large Numbers. We extend the technique of symmetrization to the case of dependent random variables and provide sequential (non-i.i.d.) analogues of various classical measures of complexity, such as covering numbers and combinatorial dimensions from empirical process theory. We establish relationships between these various sequential complexity measures and show that they provide a tight control on the uniform conv...
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作者：Cacciapuoti, Claudio; Maltsev, Anna; Schlein, Benjamin
作者单位：University of Bonn; University of Bristol
摘要：We consider ensembles of Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. We show the convergence of the Stieltjes transform towards the Stieltjes transform of the semicircle law on optimal scales and with the optimal rate. Our bounds improve previous results, in particular from ErdAs et al. (Adv Math 229(3):1435-1515, 2012; Electron J Probab 18(59):1-58, 2013), by removing the logarithmic corrections. As applications...
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作者：Calka, Pierre; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Lehigh University
摘要：Let K-n be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on . We establish variance asymptotics as for the re-scaled intrinsic volumes and -face functionals of , , resolving an open problem (Weil and Wieacker, Handbook of Convex Geometry, vol. B, pp. 1391-1438. North-Holland/Elsevier, Amsterdam, 1993). Variance asymptotics are given in terms of functionals of germ-grain models having parabolic grains with apices at a Poisson point process ...
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作者：Aizenman, Michael; Warzel, Simone
作者单位：Princeton University; Princeton University; Technical University of Munich
摘要：We consider the distribution of the values at real points of random functions which belong to the Herglotz-Pick (HP) class of analytic mappings of the upper half plane into itself. It is shown that under mild stationarity assumptions the individual values of HP functions with singular spectra have a Cauchy type distribution. The statement applies to the diagonal matrix elements of random operators, and holds regardless of the presence or not of level repulsion, i.e. applies to both random matr...
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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 .
