3-4期

最新文章

• Martingale solutions for the stochastic nonlinear Schrodinger equation in the energy space AI翻译
  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.
• Stationary coalescing walks on the lattice AI翻译
  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...
• Self-attracting self-avoiding walk AI翻译
  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 ...
• Regularization by noise for stochastic Hamilton-Jacobi equations AI翻译
  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.
• Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula AI翻译
  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, ...
• A Liouville theorem for stationary and ergodic ensembles of parabolic systems AI翻译
  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.
• Fundamental limits of symmetric low-rank matrix estimation AI翻译
  作者：Lelarge, Marc; Miolane, Leo
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Inria
  摘要：We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean squared error, while the rank of the signal remains constant. We also show that our model extends beyond the particular case of additive Gaus...
• The dimension of the boundary of super-Brownian motion AI翻译
  作者：Mytnik, Leonid; Perkins, Edwin
  作者单位：Technion Israel Institute of Technology; University of British Columbia
  摘要：We show that the Hausdorff dimension of the boundary of d-dimensional super-Brownian motion is 0, if d=1, 4-22, if d=2, and (9-17)/2, if d=3.
• On pinned fields, interlacements, and random walk on (Z/NZ)2 AI翻译
  作者：Rodriguez, Pierre-Francois
  作者单位：University of California System; University of California Los Angeles
  摘要：We define two families of Poissonian soups of bidirectional trajectories onZ2, which can be seen to adequately describe the local picture of the trace left by a random walk on the two-dimensional torus (Z/NZ)2, started from the uniform distribution, run up to a time of order (NlogN)2 and forced to avoid a fixed point. The local limit of the latter was recently established inComets et al. (Commun Math Phys 343:129-164, 2016). Our construction proceeds by considering, somewhat in the spirit of s...
• Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula (vol 174, pg 945, 2019) AI翻译
  作者：Fang, Xiao; Shao, Qi-Man; Xu, Lihu
  作者单位：Chinese University of Hong Kong; University of Macau