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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove that for any constant K >= 1, the value functions for time homogeneous stochastic differential games in the whole space can be approximated up to a constant over K by value functions whose second-order derivatives are bounded by a constant times K. On the way of proving this result we prove that the value functions for stochastic differential games in domains and in the whole space admit estimates of their Lipschitz constants in a variety of settings.
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作者：Miller, Jason; Sun, Nike; Wilson, David B.
作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Microsoft
摘要：The conformal loop ensemble CLEK is the canonical conformally invariant probability measure on noncrossing loops in a proper simply connected domain in the complex plane. The parameter K varies between 8/3 and 8; CLE8/3 is empty while CLE8 is a single space-filling loop. In this work, we study the geometry of the CLE gasket, the set of points not surrounded by any loop of the CLE. We show that the almost sure Hausdorff dimension of the gasket is bounded from below by 2 (8 K)(3K 8)/(32K) when 4...
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作者：Schuhmacher, Dominic; Stucki, Kaspar
作者单位：University of Bern; University of Gottingen
摘要：We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's meth...
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作者：Kifer, Yuri; Varadhan, S. R. S.
作者单位：Hebrew University of Jerusalem; New York University
摘要：We obtain functional central limit theorems for both discrete time expressions of the form 1/root N Sigma([Nt])(n=1) (F(X(q(1)(n)),...,X(q(l)(n))) - (F) over bar) and similar expressions in the continuous time where the sum is replaced by an integral. Here X(n), n >= 0 is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polynomial growth and certain regularity properties, (F) over bar = integral F d(mu X ... X mu...
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作者：Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We prove that the distance between two reflected Brownian motions, driven by the same white noise, outside a sphere in a 3-dimensional flat torus does not converge to 0, a.s., if the radius of the sphere is sufficiently small, relative to the size of the torus.
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作者：Ben Arous, Gerard; Bourgade, Paul
作者单位：New York University; Harvard University
摘要：This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth smallest gap, normalized by a factor n(-4/3), has a limiting density proportional to x(3k-1)e(-x3). Concerning the largest gaps, normalized by n/root log n, they converge in L-p to a constant for all p > 0. These results are compared with the extreme gaps betw...
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作者：Sethuraman, Sunder; Varadhan, S. R. S.
作者单位：University of Arizona; New York University
摘要：Laws of large numbers, starting from certain nonequilibrium measures, have been shown for the integrated current across a bond, and a tagged particle in one-dimensional symmetric nearest-neighbor simple exclusion [Ann. Inst. Henri Poincare Probab. Stat. 42 (2006) 567-577]. In this article, we prove corresponding large deviation principles and evaluate the rate functions, showing different growth behaviors near and far from their zeroes which connect with results in [J. Stat. Phys. 136 (2009) 1...
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作者：Berestycki, Julien; Berestycki, Nathanael; Schweinsberg, Jason
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; University of Cambridge; University of California System; University of California San Diego
摘要：We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (log N)(3), in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process...
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作者：Crawford, Nicholas; Sly, Allan
作者单位：Technion Israel Institute of Technology; University of California System; University of California Berkeley
摘要：We study limit laws for simple random walks on supercritical long-range percolation clusters on Z(d), d >= 1. For the long range percolation model, the probability that two vertices x, y are connected behaves asymptotically as parallel to x - y parallel to(-s)(2). When s is an element of (d, d + 1), we prove that the scaling limit of simple random walk on the infinite component converges to an a-stable Levy process with alpha = s - d establishing a conjecture of Berger and Biskup [Probab. Theo...
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作者：Adler, Robert J.; Samorodnitsky, Gennady; Taylor, Jonathan E.
作者单位：Technion Israel Institute of Technology; Cornell University; Stanford University
摘要：We consider smooth, infinitely divisible random fields (X (t), t is an element of M), M subset of R-d, with regularly varying Levy measure, and are interested in the geometric characteristics of the excursion sets A(u) = {t is an element of M : X(t) > u} over high levels u. For a large class of such random fields, we compute the u -> infinity asymptotic joint distribution of the numbers of critical points, of various types, of X in A(u), conditional on A(u) being nonempty. This allows us, for ...
