-
作者：Zhang, Yu
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：In this paper, we consider the linearly reinforced and the once-reinforced random walk models in the transient phase on trees. We show the large deviations for the upper tails for both models. We also show the exponential decay for the lower tail in the once-reinforced random walk model. However, the lower tail is in polynomial decay for the linearly reinforced random walk model.
-
作者：Rassoul-Agha, Firas; Seppaelaeinen, Timo
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider a random walk in a random potential on a square lattice of arbitrary dimension. The potential is a function of an ergodic environment and steps of the walk. The potential is subject to a moment assumption whose strictness is tied to the mixing of the environment, the best case being the i.i.d. environment. We prove that the infinite volume quenched point-to-point free energy exists and has a variational formula in terms of entropy. We establish regularity properties of the point-to...
-
作者：Berger, Noam; Deuschel, Jean-Dominique
作者单位：Hebrew University of Jerusalem; Technical University of Berlin
摘要：We consider a random walk on , in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from to nearest neighbor is the same as to nearest neighbor . Assuming that the environment is genuinely -dimensional and balanced we show a quenched invariance principle: for almost every environment, the diffusively rescaled random walk converges to a Brownian motion with deterministic non-degenerate diffusion matrix. Within the i.i.d. setting, our result extend bo...
-
作者：Nolen, James
作者单位：Duke University
摘要：We consider solutions of an elliptic partial differential equation in with a stationary, random conductivity coefficient that is also periodic with period . Boundary conditions on a square domain of width are arranged so that the solution has a macroscopic unit gradient. We then consider the average flux that results from this imposed boundary condition. It is known that in the limit , this quantity converges to a deterministic constant, almost surely. Our main result is that the law of this r...
-
作者：Hedenmalm, Haakan; Nieminen, Pekka J.
作者单位：Royal Institute of Technology; University of Helsinki
摘要：We relate the Gaussian free field on a planar domain to the variational formula of Hadamard which explains the change of the Green function under a perturbation of the domain. This is accomplished by means of a natural integral operator-called the Hadamard operator-associated with a given flow of growing domains.
-
作者：Romito, Marco
作者单位：University of Pisa
摘要：We consider the dyadic model with viscosity and additive Gaussian noise as a simplified version of the stochastic Navier-Stokes equations, with the purpose of studying uniqueness and emergence of singularities. We prove pathwise uniqueness and absence of blow-up in the intermediate intensity of the non-linearity, morally corresponding to the 3D case, and blow-up for stronger intensity. Moreover, blow-up happens with probability one for regular initial data.
-
作者：Borodin, Alexei; Corwin, Ivan
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters . We prove several results about these processes, which include the following. (1) We explicitly evaluate expectations of a rich family of observables for these processes. (2) In the case , we find a Fredholm determinant formula for a -Laplace transform of the distribution of the last part of the Macdonald-rand...
-
作者：Mourrat, Jean-Christophe
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For smooth initial condition, the rescaled solution of such an equation, once averaged over the randomness, is shown to converge polynomially fast to the solution of the homogenized equation, with an explicit exponent depending only on the dimensi...
-
作者：Paouris, Grigoris; Pivovarov, Peter; Zinn, Joel
作者单位：Texas A&M University System; Texas A&M University College Station; University of Missouri System; University of Missouri Columbia
摘要：We prove a central limit theorem for the volume of projections of the cube onto a random subspace of dimension , when is fixed and . Randomness in this case is with respect to the Haar measure on the Grassmannian manifold.
-
作者：Castillo, Ismael; Kerkyacharian, Gerard; Picard, Dominique
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：Convergence of the Bayes posterior measure is considered in canonical statistical settings where observations sit on a geometrical object such as a compact manifold, or more generally on a compact metric space verifying some conditions. A natural geometric prior based on randomly rescaled solutions of the heat equation is considered. Upper and lower bound posterior contraction rates are derived.
