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作者：Roberto, Cyril
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails in the case when spins are unbounded. The interactions are bounded and of finite range. The self-potential enters into two classes of measures, kappa-concave probability measures and sub-exponential laws, for which it is known that no exponential decay can occur. Using coercive inequalities we prove that, for kappa-concave probability measures, the associated infinite volume semi-group decays to equilibrium...
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作者：Bollobas, Bela; Riordan, Oliver
作者单位：University of Oxford; University of Cambridge; University of Memphis
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作者：Ben Arous, G.; Kargin, V.
作者单位：Stanford University
摘要：We continue here the study of free extreme values begun in Ben Arous and Voiculescu (Ann Probab 34:2037-2059, 2006). We study the convergence of the free point processes associated with free extreme values to a free Poisson random measure (Voiculescu in Lecture notes in mathematics. Springer, Heidelberg, pp. 279-349, 1998; Barndorff-Nielsen and Thorbjornsen in Probab Theory Relat Fields 131:197-228, 2005). We relate this convergence to the free extremal laws introduced in Ben Arous and Voicule...
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作者：Bobkov, Sergey G.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Isotropy-like properties are considered for finite measures with heavy tails. As a basic tool, we extend K. Ball's relationship between convex bodies and finite logarithmically concave measures to a larger class of distributions, satisfying convexity conditions of the Brunn-Minkowski type.
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作者：Schramm, Oded; Zhou, Wang
作者单位：National University of Singapore; Microsoft
摘要：This paper examines how close the chordal SLEk curve gets to the real line asymptotically far away from its starting point. In particular, when k is an element of (0, 4), it is shown that if beta > beta(k) := 1/(8/k - 2), then the intersection of the SLEk curve with the graph of the function y = x/(log x)(beta), x > e, is a.s. bounded, while it is a.s. unbounded if beta = beta(k). The critical SLE4 curve a.s. intersects the graph of y = x(-(log log x)alpha), x > e(e), in an unbounded set if al...
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作者：Zhang, Xicheng
作者单位：Huazhong University of Science & Technology; University of New South Wales Sydney
摘要：By reversing the time variable we derive a stochastic representation for backward incompressible Navier-Stokes equations in terms of stochastic Lagrangian paths, which is similar to Constantin and Iyer's forward formulations in Constantin and Iyer (Comm Pure Appl Math LXI:330-345, 2008). Using this representation, a self-contained proof of local existence of solutions in Sobolev spaces are provided for incompressible Navier-Stokes equations in the whole space. In two dimensions or large viscos...
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作者：Levin, David A.; Luczak, Malwina J.; Peres, Yuval
作者单位：University of Oregon; University of London; London School Economics & Political Science; Microsoft; University of Washington; University of Washington Seattle; University of California System; University of California Berkeley
摘要：We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie-Weiss Model. For beta < 1, we prove that the dynamics exhibits a cut-off: the distance to stationarity drops from near 1 to near 0 in a window of order n centered at [2(1 - beta)](-1)n log n. For beta = 1, we prove that the mixing time is of order n(3/2). For beta > 1, we study metastability. In particular, we show that the Glauber dynamics restricted to states of non-negative magnetization has mix...
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作者：Cattiaux, Patrick; Guillin, Arnaud; Wu, Li-Ming
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA)
摘要：We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient conditions work even in the case where the Bakry-Emery curvature is not lower bounded. Several new examples are provided.
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作者：Jia, Guangyan; Peng, Shige
作者单位：Shandong University
摘要：A real valued function h defined on R is called g-convex if it satisfies the generalized Jensen's inequality for a given g-expectation, i.e., h (E-g[X]) <= E-g [h (X)] holds for all random variables X such that both sides of the inequality are meaningful. In this paper we will give a necessary and sufficient condition for a C (2)-function being g-convex, and study some more general situations. We also study g-concave and g-affine functions, and a relation between g-convexity and backward stoch...
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作者：Fang, Shizan; Shao, Jinghai; Sturm, Karl-Theodor
作者单位：University of Bonn; Universite Bourgogne Europe; Beijing Normal University
摘要：The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel-stunel. Carrying out the program of Ambrosio-Gigli-Savar,, we present a complete characterization of the derivative processes for certain class of absolutely continuous curves. We prove existence of the gradient flow curves for the relative entropy w.r.t. the Wiener measure and identify these gradient flow curves ...
