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作者：Landim, C; Neto, JN
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider reversible, conservative Ginzburg-Landau processes in a random environment, whose potential are bounded perturbations of the Gaussian potential, evolving on a d-dimensional cube of length L. We prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order L-2 almost surely with respect to the environment.
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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.
