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作者：Hansen, Wolfhard
作者单位：University of Bielefeld
摘要：The 3G-inequality for Green functions g(D) on arbitrary bounded domains in R-2, which Bass and Burdzy (Probab Theory Relat Fields 101(4): 479- 493, 1995) obtained by a genuinely probabilistic proof (using loops of Brownian motion around the origin), is proven (in a more precise form) employing elementary properties of harmonic measures only. Since harmonic measures are hitting distributions of Brownian motion, this purely analytic proof can be viewed as well as being probabilistic. A spin- off...
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作者：Mossel, Elchanan
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Weizmann Institute of Science
摘要：Arrow's Impossibility theorem states that any constitution which satisfies independence of irrelevant alternatives (IIA) and unanimity and is not a dictator has to be non-transitive. In this paper we study quantitative versions of Arrow theorem. Consider n voters who vote independently at random, each following the uniform distribution over the six rankings of three alternatives. Arrow's theorem implies that any constitution which satisfies IIA and unanimity and is not a dictator has a probabi...
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作者：Bartlett, Peter L.; Mendelson, Shahar; Neeman, Joseph
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Technion Israel Institute of Technology
摘要：We study the predictive performance of a (1)-regularized linear regression in a model-free setting, including the case where the number of covariates is substantially larger than the sample size. We introduce a new analysis method that avoids the boundedness problems that typically arise in model-free empirical minimization. Our technique provides an answer to a conjecture of Greenshtein and Ritov (Bernoulli 10(6):971-988, 2004) regarding the persistence rate for linear regression and allows u...
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作者：Deya, A.; Gubinelli, M.; Tindel, S.
作者单位：Universite PSL; Universite Paris-Dauphine; Universite de Lorraine
摘要：This article is devoted to define and solve an evolution equation of the form dy (t) = Delta y (t) dt + dX (t) (y (t) ), where Delta stands for the Laplace operator on a space of the form , and X is a finite dimensional noisy nonlinearity whose typical form is given by , where each x = (x ((1)), aEuro broken vertical bar , x ((N))) is a gamma-Holder function generating a rough path and each f (i) is a smooth enough function defined on . The generalization of the usual rough path theory allowin...
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作者：Montanari, Andrea; Mossel, Elchanan; Sly, Allan
作者单位：Stanford University; Stanford University; Weizmann Institute of Science; University of California System; University of California Berkeley; University of California System; University of California Berkeley; Microsoft
摘要：We consider the Ising model with inverse temperature beta and without external field on sequences of graphs G (n) which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weakly converges to the symmetric mixture of the Ising model with + boundary conditions and the - boundary conditions on the k-regular tree with inverse temperature beta. In the case where the graphs G (n) are expanders we derive a more detailed understanding by showing convergence ...
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作者：Guo, Xiaoqin; Zeitouni, Ofer
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：We consider random walks in a balanced random environment in Z(d), d >= 2. We first prove an invariance principle ( for d >= 2) and the transience of the random walks when d >= 3 (recurrence when d = 2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.
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作者：Hairer, Martin
作者单位：University of Warwick
摘要：We consider a class of singular perturbations to the stochastic heat equation or semilinear variations thereof. The interesting feature of these perturbations is that, as the small parameter epsilon tends to zero, their solutions converge to the 'wrong' limit, i.e. they do not converge to the solution obtained by simply setting epsilon = 0. A similar effect is also observed for some (formally) small stochastic perturbations of a deterministic semilinear parabolic PDE. Our proofs are based on a...
