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作者：Delmotte, T; Deuschel, JD
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Technical University of Berlin
摘要：We consider diffusions on R-d or random walks on Z(d) in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients. We show existence and Holder continuity of second space derivatives and time derivatives for the annealed kernels of such diffusions and give estimates for these derivatives. In the case of random walks, these estimates are applied to the Ginzburg-Landau del phi interface model.
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作者：Liorit, G
作者单位：Universite de Poitiers
摘要：A kind of Laplace's method is developped for iterated stochastic integrals where integrators are complex standard Brownian motions. Then it is used to extend properties of Bougerol and Jeulin's path transform in the random case when simple representations of complex semisimple Lie algebras are not supposed to be minuscule.
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作者：Guionnet, A; Maïda, M
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The estimation of various matrix integrals as the size of the matrices goes to infinity is motivated by theoretical physics, geometry and free probability questions. On a rigorous ground, only integrals of one matrix or of several matrices with simple quadratic interaction (called AB interaction) could be evaluated so far (see e.g. [19], [17] or [9]). In this article, we follow an idea widely developed in the physics literature, which is based on character expansion, to study more complex inte...
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作者：Gallardo, L; Yor, M
作者单位：Universite de Tours; Sorbonne Universite; Universite Paris Cite
摘要：In this paper we give a sufficient condition on the semi group densities of an homogeneous Markov process taking values in R-n which ensures that it enjoys the time-inversion property. Our condition covers all previously known examples of Markov processes satisfying this property. As new examples we present a class of Markov processes with jumps, the Dunkl processes and their radial parts.
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作者：Burdzy, K; Mytnik, L
作者单位：University of Washington; University of Washington Seattle; Technion Israel Institute of Technology
摘要：We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the super-Brownian motion with reflecting historical paths. This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits-they obviously hold for the unique limit found in the present paper.
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作者：Cerrai, S
作者单位：University of Florence; Scuola Normale Superiore di Pisa
摘要：We prove uniqueness, ergodicity and strongly mixing property of the invariant measure for a class of stochastic reaction-diffusion equations with multiplicative noise, in which the diffusion term in front of the noise may vanish and the deterministic part of the equation is not necessary asymptotically stable. To this purpose, we show that the L-1-norm of the difference of two solutions starting from any two different initial data converges P-a.s. to zero, as time goes to infinity.
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作者：Li, ZH; Wang, H; Xiong, J
作者单位：University of Oregon; Beijing Normal University; University of Tennessee System; University of Tennessee Knoxville; University of Alberta
摘要：The scaling limit for a class of interacting superprocesses and the associated singular, degenerate stochastic partial differential equation (SDSPDE) are investigated. It is proved that the scaling limit is a coalescing, purely-atomic-measure-valued process which is the unique strong solution of a reconstructed, associated SDSPDE.
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作者：Linusson, S; Wästlund, J
作者单位：Linkoping University
摘要：An assignment problem is the optimization problem of finding, in an m by n matrix of nonnegative real numbers, k entries, no two in the same row or column, such that their sum is minimal. Such an optimization problem is called a random assignment problem if the matrix entries are random variables. We give a formula for the expected value of the optimal k-assignment in a matrix where some of the entries are zero, and all other entries are independent exponentially distributed random variables w...
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作者：Zhan, DP
作者单位：California Institute of Technology
摘要：This paper introduces the annulus SLEkappa processes in doubly connected domains. Annulus SLE6 has the same law as stopped radial SLE6, up to a time-change. For kappa not equal 6, some weak equivalence relation exists between annulus SLEkappa and radial SLEkappa. Annulus SLE2 is the scaling limit of the corresponding loop-erased conditional random walk, which implies that a certain form of SLE2 satisfies the reversibility property. We also consider the disc SLEkappa process defined as a limiti...
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作者：Bakhtin, V; Kifer, Y
作者单位：Belarusian State University; Hebrew University of Jerusalem
摘要：In systems which combine fast and slow motions it is usually impossible to study directly corresponding two scale equations and the averaging principle suggests to approximate the slow motion by averaging in fast variables. We consider the averaging setup when both fast and slow motions are diffusion processes depending on each other (fully coupled) and show that there exists a diffusion process which approximates the slow motion in the L-2 sense much better than the averaged motion prescribed...
