Probability Theory and Related Fields

最新文章

• Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times AI翻译
  作者：Peres, Yuval; Stauffer, Alexandre; Steif, Jeffrey E.
  作者单位：Microsoft; University of Bath; Chalmers University of Technology; University of Gothenburg
  摘要：We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph are either open or closed and refresh their status at rate while at the same time a random walker moves on at rate 1 but only along edges which are open. On the -dimensional torus with side length , we prove that in the subcritical regime, the mixing times for both the full system and the random walker are up to constants. We also obtain results concerning mean squared displacement and hitting ti...
• Anomalous shock fluctuations in TASEP and last passage percolation models AI翻译
  作者：Ferrari, Patrik L.; Nejjar, Peter
  作者单位：University of Bonn
  摘要：We consider the totally asymmetric simple exclusion process with initial conditions and/or jump rates such that shocks are generated. If the initial condition is deterministic, then the shock at time will have a width of order . We determine the law of particle positions in the large time limit around the shock in a few models. In particular, we cover the case where at both sides of the shock the process of the particle positions is asymptotically described by the Airy process. The limiting di...
• Transfer current and pattern fields in spanning trees AI翻译
  作者：Kassel, Adrien; Wu, Wei
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Brown University
  摘要：When a simply connected domain () is approximated in a good way by embedded connected weighted graphs, we prove that the transfer current matrix (defined on the edges of the graph viewed as an electrical network) converges, up to a local weight factor, to the differential of Green's function on . This observation implies that properly rescaled correlations of the spanning tree model and correlations of minimal subconfigurations in the abelian sandpile model have a universal and conformally cov...
• Law of iterated logarithm and invariance principle for one-parameter families of interval maps AI翻译
  作者：Schnellmann, Daniel
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We show that for almost every map in a transversal one-parameter family of piecewise expanding unimodal maps the Birkhoff sum of suitable observables along the forward orbit of the turning point satisfies the law of iterated logarithm. This result will follow from an almost sure invariance principle for the Birkhoff sum, as a function on the parameter space. Furthermore, we obtain a similar result for general one-parameter families of piecewise expanding maps on the interval.
• The conformal loop ensemble nesting field AI翻译
  作者：Miller, Jason; Watson, Samuel S.; Wilson, David B.
  作者单位：Massachusetts Institute of Technology (MIT); Microsoft; Microsoft
  摘要：The conformal loop ensemble with parameter is the canonical conformally invariant measure on countably infinite collections of non-crossing loops in a simply connected domain. We show that the number of loops surrounding an -ball (a random function of and ) minus its expectation converges almost surely as to a random conformally invariant limit in the space of distributions, which we call the nesting field. We generalize this result by assigning i.i.d. weights to the loops, and we treat an alt...
• Uniqueness of gradient Gibbs measures with disorder AI翻译
  作者：Cotar, Codina; Kuelske, Christof
  作者单位：University of London; University College London; Ruhr University Bochum
  摘要：We consider-in a uniformly strictly convex potential regime-two versions of random gradient models with disorder. In model (A) the interface feels a bulk term of random fields while in model (B) the disorder enters through the potential acting on the gradients. We assume a general distribution on the disorder with uniformly-bounded finite second moments. It is well known that for gradient models without disorder there are no Gibbs measures in infinite volume in dimension , while there are shif...
• Comparison and anti-concentration bounds for maxima of Gaussian random vectors AI翻译
  作者：Chernozhukov, Victor; Chetverikov, Denis; Kato, Kengo
  作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles; University of Tokyo
  摘要：Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical process and extreme value theories. Here we give explicit comparisons of expectations of smooth functions and distribution functions of maxima of Gaussian random vectors without any restriction on the covariance matrices. We also establish an anti-concentration...
• The parabolic Anderson model in a dynamic random environment: space-time ergodicity for the quenched Lyapunov exponent AI翻译
  作者：Erhard, D.; den Hollander, F.; Maillard, G.
  作者单位：Leiden University; Leiden University - Excl LUMC; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite
  摘要：We continue our study of the parabolic Anderson equation , where is the diffusion constant, is the discrete Laplacian, and plays the role of a dynamic random environment that drives the equation. The initial condition , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate , split into two at rate , and die at rate . We assu...
• On the concentration of random multilinear forms and the universality of random block matrices AI翻译
  作者：Nguyen, Hoi H.; O'Rourke, Sean
  作者单位：University System of Ohio; Ohio State University; Yale University
  摘要：The circular law asserts that if is a matrix with iid complex entries of mean zero and unit variance, then the empirical spectral distribution of converges almost surely to the uniform distribution on the unit disk as tends to infinity. Answering a question of Tao, we prove the circular law for a general class of random block matrices with dependent entries. The proof relies on an inverse-type result for the concentration of linear operators and multilinear forms.
• Hypoellipticity for filtering problems of partially observable diffusion processes AI翻译
  作者：Krylov, N. V.
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：We prove that under Hormander's type conditions on the coefficients of the unobservable component of a partially observable diffusion process the filtering density is infinitely differentiable and can be represented as the integral of an infinitely differentiable kernel against the prior initial distribution. These results are derived from more general results obtained for SPDEs. One of the main novelties of the paper is the existence and smoothness of the kernel, another one is that we allow ...