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作者：Landim, C; Yau, HT
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); New York University
摘要：We consider the Ginzburg-Landau process on the lattice Z(d) whose potential is a bounded perturbation of the Gaussian potential. We prove that the decay rate to equilibrium in the variance sense is t(-d/2) up to a logarithmic correction, for any function a with finite triple norm; that is, \\\u\\\ = Sigma(xis an element ofzd) \\partial derivative(etax)u\\(infinity) < infinity.
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作者：Sethuraman, S
作者单位：Iowa State University
摘要：Resolvent H-1 norms with respect to simple exclusion processes play an important role in many problems with respect to additive functionals, tagged particles, and hydrodynamics, among other concerns. Here, general translation-invariant finite-range simple exclusion processes with and without a distinguished particle are considered. For the standard system of indistinguishable particles, it is proved that the corresponding H-1 norms are equivalent, in a sense, to the H-1 norms of a nearest-neig...
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作者：Tolmatz, L
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作者：Hara, T; Van Der Hofstad, R; Slade, G
作者单位：Nagoya University; University of British Columbia; Delft University of Technology; Eindhoven University of Technology
摘要：We consider spread-out models of self-avoiding walk, bond percolation, lattice trees and bond lattice animals on Z(d), having long finite-range connections, above their upper critical dimensions d = 4 (self-avoiding walk), d = 6 (percolation) and d = 8 (trees and animals). The two-point functions for these models are respectively the generating function for self-avoiding walks from the origin to X E Zd, the probability of a connection from 0 to x, and the generating function for lattice trees ...
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作者：Burdzy, K; Kulczycki, T
作者单位：University of Washington; University of Washington Seattle; Polish Academy of Sciences; Wroclaw University of Science & Technology
摘要：Let X(t) be the symmetric alpha-stable process in R-d, alpha is an element of (0, 2), d greater than or equal to 2. For f:(0, 1) --> (0, infinity) let D (f) be the thorn {x is an element of R-d : x(1) is an element of (0, 1), \(x(2), - - -, x(d))\ < f (x(1))}. We give an integral criterion in terms of f for the existence of a random time s such that X(t) remains in X(s) + (D) over bar (f) for all t is an element of [s, s + 1).
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作者：Benjamini, I; Häggström, O; Peres, Y; Steif, JE
作者单位：University of Gothenburg; University of California System; University of California Berkeley; Hebrew University of Jerusalem; University System of Georgia; Georgia Institute of Technology; Chalmers University of Technology
摘要：Consider a sequence of i.i.d. random variables, where each variable is refreshed (i.e., replaced by an independent variable with the same law) independently, according to a Poisson clock. At any fixed time t, the resulting sequence has the same law as at time 0, but there can be exceptional random times at which certain almost sure properties of the time 0 sequence are violated. We prove that there are no such exceptional times for the law of large numbers and the law of the iterated logarithm...
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作者：Choirat, C; Hess, C; Seri, R
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：In this paper, we prove a new version of the Birkhoff ergodic theorem (BET) for random variables depending on a parameter (alias integrands). This involves variational convergences, namely epigraphical, hypographical and uniform convergence and requires a suitable definition of the conditional expectation of integrands. We also have to establish the measurability of the epigraphical lower and upper limits with respect to the or-field of invariant subsets. From the main result, applications to ...
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作者：Zambotti, L
作者单位：Scuola Normale Superiore di Pisa
摘要：We study a white-noise driven semilinear partial differential equation on the spatial interval [0, 1] with Dirichlet boundary condition and with a singular drift of the form cu(-3), c > 0. We prove existence and uniqueness of a non-negative continuous adapted solution u on [0, infinity) x [0, 1] for every nonnegative continuous initial datum x, satisfying x(0) = x(1) = 0. We prove that the law pi(delta) of the Bessel bridge on [0, 1] of dimension delta > 3 is the unique invariant probability m...
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作者：Seppäläinen, T; Sethuraman, S
作者单位：University of Wisconsin System; University of Wisconsin Madison; Iowa State University
摘要：Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with nonzero drift. Let the process be stationary with product Bernoulli invariant distribution at density rho. Place a second-class particle initially at the origin. For the case rho not equal 1/2 we show that the time spent by the second-class particle at the origin has finite expectation. This strong transience is then used to prove that variances of additive functionals of local mean-zero functi...
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作者：Guillin, A
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：Consider the following stochastic differential equation in R-d: dX(t)(epsilon) = b(X-t(epsilon), xi(t/epsilon)) dt + rootepsilona(X-t(epsilon), xi(t/epsilon)) dW(t), X-0(epsilon) = X-0, where the random environment (xi(t)) is an exponentially ergodic Markov process, independent of the Wiener process (W-t), with invariant probability measure pi, and epsilon is some small parameter. In this paper we prove the moderate deviations for the averaging principle of X-epsilon, that is, deviations of (X...
