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作者：Fribergh, Alexander; Gantert, Nina; Popov, Serguei
作者单位：University of Munster; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universidade de Sao Paulo
摘要：We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n (kappa) ) from the origin, kappa is an element of (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order ...
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作者：Delbaen, Freddy; Tang, Shanjian
作者单位：Fudan University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations in R-p (p is an element of [1, infinity)) and backward stochastic differential equations (BSDEs) in R-p x H-p (p is an element of (1, infinity)) and in R-infinity x (L-infinity) over bar (BMO), with the coefficients being allowed to be unbounded. In particular, the probabilistic version of Fefferman's inequality plays a crucial role in the development of our theory, which seems to be new. Se...
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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...
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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...
