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作者：Brzezniak, Zdzislaw; Hornung, Fabian; Weis, Lutz
作者单位：University of York - UK; Helmholtz Association; Karlsruhe Institute of Technology
摘要：We consider a stochastic nonlinear Schrodinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing Stochastic NLSE in H1 on compact manifolds and bounded domains. We construct a martingale solution using a modified Faedo-Galerkin-method based on the Littlewood-Paley-decomposition. For the 2d manifolds with bounded geometry, we use the Strichartz estimates to show the pathwise uniqueness of solutions.
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作者：Chaika, Jon; Krishnan, Arjun
作者单位：Utah System of Higher Education; University of Utah; University of Rochester
摘要：We consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice. We assume that once walks meet, they coalesce. In 2d, we classify the collective behavior of these walks under mild assumptions: they either coalesce almost surely or form bi-infinite trajectories. Bi-infinite trajectories form measure-preserving dynamical systems, have a common asymptotic direction in 2d, and possess other nice properties. We use our theory to classify the be...
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作者：Hammond, Alan; Helmuth, Tyler
作者单位：University of California System; University of California Berkeley; University of Bristol
摘要：This article is concerned with self-avoiding walks (SAW) on that are subject to a self-attraction. The attraction, which rewards instances of adjacent parallel edges, introduces difficulties that are not present in ordinary SAW. Ueltschi has shown how to overcome these difficulties for sufficiently regular infinite-range step distributions and weak self-attractions (Ueltschi in Probab Theory Relat Fields 124(2):189-203, 2002). This article considers the case of bounded step distributions. For ...
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作者：Chen, Xinxin; He, Hui
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Beijing Normal University
摘要：Given a branching random walk on R started from the origin, where the tail of the branching law decays at least exponentially fast and the offspring number is at least one, let Z(n)(.) be the counting measure which counts the number of individuals at the n-th generation located in a given set. Under some mild conditions, it is known (Biggins in Stoch. Process. Appl. 34:255-274, 1990) that for any interval A subset of R, Z(n)(root nA)/Z(n)(R) converges a.s. to nu(A), where nu is the standard Ga...
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作者：Dembo, Amir; Huang, Ruojun; Zheng, Tianyi
作者单位：Stanford University; Stanford University; University of California System; University of California San Diego
摘要：For any graph having a suitable uniform Poincare inequality and volume growth regularity, we establish two-sided Gaussian transition density estimates and parabolic Harnack inequality, for constant speed continuous time random walks evolving via time varying, uniformly elliptic conductances, provided the vertex conductances (i.e. reversing measures), increase in time. Such transition density upper bounds apply for discrete time uniformly lazy walks, with the matching lower bounds holding once ...
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作者：Gassiat, Paul; Gess, Benjamin
作者单位：Universite PSL; Universite Paris-Dauphine; Max Planck Society; University of Bielefeld
摘要：We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path L bounds for the second derivative of solutions to such PDE are shown. These bounds are expressed as solutions to reflected SDE and are shown to be optimal.
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作者：Buckingham, Robert; Liechty, Karl
作者单位：DePaul University; University System of Ohio; University of Cincinnati
摘要：The tacnode process is a universal behavior arising in nonintersecting particle systems and tiling problems. For Dyson Brownian bridges, the tacnode process describes the grazing collision of two packets of walkers. We consider such a Dyson sea on the unit circle with drift. For any k is an element of Z, we show that an appropriate double scaling of the drift and return time leads to a generalization of the tacnode process in which k particles are expected to wrap around the circle. We derive ...
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作者：Freidlin, Mark; Koralov, Leonid; Wentzell, Alexander
作者单位：University System of Maryland; University of Maryland College Park; Tulane University
摘要：We consider diffusion processes in media with pockets of large diffusivity. The asymptotic behavior of such processes is described when the diffusion coefficients in the pockets tend to infinity. The limiting process is identified as a diffusion on the space where each of the pockets is treated as a single point, and certain conditions on the behavior of the process on the boundary of the pockets are imposed. Calculation of various probabilities and expectations related to the limiting process...
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作者：Fang, Xiao; Shao, Qi-Man; Xu, Lihu
作者单位：Chinese University of Hong Kong; University of Macau
摘要：Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order derivatives. For a class of multivariate limiting distributions, we use Bismut's formula in Malliavin calculus to control the derivatives of the Stein equation solutions by the first derivative of the test function. Combined with Stein's exchangeable pair approach, ...
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作者：Bella, Peter; Chiarini, Alberto; Fehrman, Benjamin
作者单位：Leipzig University; Aix-Marseille Universite; Max Planck Society
摘要：A first-order Liouville theorem is obtained for random ensembles of uniformly parabolic systems under the mere qualitative assumptions of stationarity and ergodicity. Furthermore, the paper establishes, almost surely, an intrinsic large-scale C1,-regularity estimate for caloric functions.
