-
作者：Lu, Jianfeng; Nolen, James
作者单位：Duke University; Duke University
摘要：We study the trajectories of a solution to an It stochastic differential equation in , as the process passes between two disjoint open sets, and . These segments of the trajectory are called transition paths or reactive trajectories, and they are of interest in the study of chemical reactions and thermally activated processes. In that context, the sets and represent reactant and product states. Our main results describe the probability law of these transition paths in terms of a transition pat...
-
作者：Arratia, Richard; Baxendale, Peter
作者单位：University of Southern California
摘要：Under the assumption that the distribution of a nonnegative random variable admits a bounded coupling with its size biased version, we prove simple and strong concentration bounds. In particular the upper tail probability is shown to decay at least as fast as the reciprocal of a Gamma function, guaranteeing a moment generating function that converges everywhere. The class of infinitely divisible distributions with finite mean, whose L,vy measure is supported on an interval contained in for som...
-
作者：Bhatnagar, Nayantara; Peled, Ron
作者单位：University of Delaware; Tel Aviv University
摘要：We study the length of the longest increasing and longest decreasing subsequences of random permutations drawn from the Mallows measure. Under this measure, the probability of a permutation is proportional to where is a real parameter and is the number of inversions in . The case corresponds to uniformly random permutations. The Mallows measure was introduced by Mallows in connection with ranking problems in statistics. We determine the typical order of magnitude of the lengths of the longest ...
-
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...
