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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：Pitman, Jim; Ross, Nathan
作者单位：University of California System; University of California Berkeley
摘要：This article contains both a point process and a sequential description of the greatest convex minorant of Brownian motion on a finite interval. We use these descriptions to provide new analysis of various features of the convex minorant such as the set of times where the Brownian motion meets its minorant. The equivalence of these descriptions is non-trivial, which leads to many interesting identities between quantities derived from our analysis. The sequential description can be viewed as a ...
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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：Bigot, Jeremie; Loubes, Jean-Michel; Vimond, Myriam
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
摘要：In this paper we focus on estimating the deformations that may exist between similar images in the presence of additive noise when a reference template is unknown. The deformations are modeled as parameters lying in a finite dimensional compact Lie group. A general matching criterion based on the Fourier transform and its well known shift property on compact Lie groups is introduced. M-estimation and semiparametric theory are then used to study the consistency and asymptotic normality of the r...
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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：Guionnet, Alice; Zeitouni, Ofer
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Normale Superieure de Lyon (ENS de LYON); Weizmann Institute of Science
摘要：We study the eigenvalues of non-normal square matrices of the form A (n) = U (n) T (n) V (n) with U (n) , V (n) independent Haar distributed on the unitary group and T (n) real diagonal. We show that when the empirical measure of the eigenvalues of T (n) converges, and T (n) satisfies some technical conditions, all these eigenvalues lie in a single ring.
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作者：Borgs, Christian; Chayes, Jennifer T.; Tetali, Prasad
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology; Microsoft
摘要：We study two widely used algorithms for the Potts model on rectangular subsets of the hypercubic lattice Z(d)-heat bath dynamics and the Swendsen-Wang algorithm-and prove that, under certain circumstances, the mixing in these algorithms is torpid or slow. In particular, we show that for heat bath dynamics throughout the region of phase coexistence, and for the Swendsen-Wang algorithm at the transition point, the mixing time in a box of side length L with periodic boundary conditions has upper ...
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作者：van den Berg, J.; Jonasson, J.
作者单位：Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam; Chalmers University of Technology; University of Gothenburg
摘要：The BK inequality (van den Berg and Kesten in J Appl Probab 22:556-569, 1985) says that, for product measures on {0, 1} (n) , the probability that two increasing events A and B 'occur disjointly' is at most the product of the two individual probabilities. The conjecture in van den Berg and Kesten (1985) that this holds for all events was proved by Reimer (Combin Probab Comput 9:27-32, 2000). Several other problems in this area remained open. For instance, although it is easy to see that non-pr...
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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.
