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作者：Basak, Anirban; Zeitouni, Ofer
作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; Weizmann Institute of Science; New York University
摘要：Consider an N x N Toeplitz matrix T-N with symbol a(lambda) := Sigma(d1)(l=-d2) a(e)lambda(e), perturbed by an additive noise matrix N-gamma E-N, where the entries of E-N are centered i.i.d. random variables of unit variance and gamma > 1/2. It is known that the empirical measure of eigenvalues of the perturbed matrix converges weakly, as N -> infinity, to the law of a(U), where U is distributed uniformly on S-1. In this paper, we consider the outliers, i.e. eigenvalues that are at a positive ...
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作者：Helmuth, Tyler; Perkins, Will; Regts, Guus
作者单位：University of Bristol; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Amsterdam
摘要：We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice Zd and on the torus (Z/nZ)d. Our approach is based on combining contour representations from Pirogov-Sinai theory with Barvinok's approach to approximate counting using truncated Taylor series. Some consequences of our main results include an FPTAS for approximating the partition function of the hard-cor...
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作者：Adhikari, Arka; Huang, Jiaoyang
作者单位：Harvard University
摘要：In this paper, we compare the solutions of the Dyson Brownian motion for general beta and potential V and the associated McKean-Vlasov equation near the edge. Under suitable conditions on the initial data and the potential V, we obtain optimal rigidity estimates of particle locations near the edge after a short time t = o(1). Our argument uses the method of characteristics along with a careful estimate involving an equation of the edge. With the rigidity estimates as an input, we prove a centr...
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作者：Chinot, Geoffrey; Lecue, Guillaume; Lerasle, Matthieu
摘要：We obtain estimation and excess risk bounds for Empirical Risk Minimizers (ERM) and minmax Median-Of-Means (MOM) estimators based on loss functions that are both Lipschitz and convex. Results for the ERM are derived under weak assumptions on the outputs and subgaussian assumptions on the design as in Alquier et al. (Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functions. arXiv:1702.01402, 2017). The difference with Alquier et al. (2017) is that ...
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作者：Osada, Hirofumi; Tanemura, Hideki
作者单位：Kyushu University; Keio University
摘要：We present general theorems solving the long-standing problem of the existence and pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential equations (ISDEs) called interacting Brownian motions. These ISDEs describe the dynamics of infinitely-many Brownian particles moving in R-d with free potential Phi and mutual interaction potential Psi. We apply the theorems to essentially all interaction potentials of Ruelle's class such as the Lennard-Jones 6-12 potential a...
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作者：Beiglboeck, Mathias; Cox, Alexander M. G.; Huesmann, Martin
作者单位：University of Vienna; University of Bath
摘要：The Skorokhod Embedding Problem is one of the classical problems in the theory of stochastic processes, with applications in many different fields [cf. the surveys (Hobson in: Paris-Princeton lectures on mathematical finance 2010, Volume 2003 of Lecture Notes in Mathematics, Springer, Berlin, 2011; Oboj in: Probab Surv 1:321-390, 2004)]. Many of these applications have natural multi-marginal extensions leading to the (optimal) multi-marginal Skorokhod problem. Some of the first papers to consi...
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作者：Peres, Yuval; Sousi, Perla; Steif, Jeffrey E.
作者单位：Microsoft; University of Cambridge; Chalmers University of Technology; University of Gothenburg
摘要：We consider dynamical percolation on the d-dimensional discrete torus Zndof side length n, where each edge refreshes its status at rate mu=mu n <= 1/2 to be open with probability p. We study random walk on the torus, where the walker moves at rate 1 / (2d) along each open edge. In earlier work of two of the authors with A. Stauffer, it was shown that in the subcritical case p1/2. When theta(p)>0, we prove a version of this conjecture for an alternative notion of mixing time involving randomise...
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作者：Belius, David; Rosen, Jay; Zeitouni, Ofer
作者单位：University of Basel; City University of New York (CUNY) System; College of Staten Island (CUNY); Weizmann Institute of Science; New York University
摘要：Let CE,S2 denote the cover time of the two dimensional sphere by a Wiener sausage of radius E. We prove that CE,S2AS2 pi logE-1-loglogE-1is tight, where AS2=4 pi denotes the Riemannian area of S2.
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作者：Bertoin, Jean
作者单位：University of Zurich
摘要：A reinforcement algorithm introduced by Simon (Biometrika 42(3/4):425-440, 1955) produces a sequence of uniform random variables with long range memory as follows. At each step, with a fixed probability p is an element of (0, 1), (U) over cap (n+1) is sampled uniformly from (U) over cap (1), ... , (U) over cap (n), and with complementary probability 1 - p, (U) over cap (n+1) is a new independent uniform variable. The Glivenko-Cantelli theorem remains valid for the reinforced empirical measure,...
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作者：Eldan, Ronen; Mikulincer, Dan
作者单位：Weizmann Institute of Science
摘要：We prove stability estimates for the Shannon-Stam inequality (also known as the entropy-power inequality) for log-concave random vectors in terms of entropy and transportation distance. In particular, we give the first stability estimate for general log-concave random vectors in the following form: for log-concave random vectors X, Y. Rd, the deficit in the Shannon-Stam inequality is bounded from below by the expression C (D(X||G) + D(Y ||G)), where D(. ||G) denotes the relative entropy with r...
