-
作者：Kotelenez, Peter M.; Kurtz, Thomas G.
作者单位：University System of Ohio; Case Western Reserve University; University of Wisconsin System; University of Wisconsin Madison
摘要：A class of quasilinear stochastic partial differential equations (SPDEs), driven by spatially correlated Brownian noise, is shown to become macroscopic (i.e., deterministic), as the length of the correlations tends to 0. The limit is the solution of a quasilinear partial differential equation. The quasilinear SPDEs are obtained as a continuum limit from the empirical distribution of a large number of stochastic ordinary differential equations (SODEs), coupled though a mean-field interaction an...
-
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...
-
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...
-
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.
-
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...
-
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...
-
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.
-
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...
-
作者：Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing; Hairer, Martin
作者单位：University of Washington; University of Washington Seattle; University of Connecticut; University of Warwick
摘要：Consider reflecting Brownian motion in a bounded domain in R-d that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusio...
-
作者：Chatterjee, Sourav; Pal, Soumik
作者单位：Cornell University; University of California System; University of California Berkeley
摘要：Consider a time-varying collection of n points on the positive real axis, modeled as Exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If at each time point we divide the points by their sum, under suitable assumptions the rescaled point process converges to a stationary distribution (depending on n and the vector of drifts) as time goes to infinity. This stationary distribution can be exactly...
