3-4期

最新文章

• Meteor process on AI翻译
  作者：Burdzy, Krzysztof
  作者单位：University of Washington; University of Washington Seattle
  摘要：The meteor process is a model for mass redistribution on a graph. The case of finite graphs was analyzed in Billey et al. (On meteors, earthworms and WIMPs. Ann Appl Probab, 2014). This paper is devoted to the meteor process on . The process is constructed and a stationary distribution is found. Convergence to this stationary distribution is proved for a large family of initial distributions. The first two moments of the mass distribution at a vertex are computed for the stationary distributio...
• Cylinders' percolation in three dimensions AI翻译
  作者：Hilario, M. R.; Sidoravicius, V.; Teixeira, A.
  作者单位：Universidade Federal de Minas Gerais; University of Geneva; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We study the complementary set of a Poissonian ensemble of infinite cylinders in , for which an intensity parameter controls the amount of cylinders to be removed from the ambient space. We establish a non-trivial phase transition, for the existence of an unbounded connected component of this set, as crosses a critical non-degenerate intensity . We moreover show that this complementary set percolates in a sufficiently thick slab, in spite of the fact that it does not percolate in any given pla...
• Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order AI翻译
  作者：Adamczak, Radoslaw; Wolff, Pawel
  作者单位：University of Warsaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
  摘要：Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lataa we provide a concentration inequality for not necessarily Lipschitz functions with bounded derivatives of higher orders, which holds when the underlying measure satisfies a family of Sobolev type inequalities Such Sobolev type inequalities hold, e.g., if the underlying measure satisfies the log-Sobolev inequality (in which case ) or the Poincar, inequality (then ). Our concent...
• Elliptic determinantal process of type A AI翻译
  作者：Katori, Makoto
  作者单位：Chuo University
  摘要：We introduce an elliptic extension of Dyson's Brownian motion model, which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle. Using elliptic determinant evaluations related to the reduced affine root system of type , we give determinantal martingale representation (DMR) for the process, when it is started at the configuration with equidistant spacing on the circle. DMR proves that the process is determinantal and the spatio-temporal correlation kerne...
• Hierarchical exchangeability of pure states in mean field spin glass models AI翻译
  作者：Panchenko, Dmitry
  作者单位：Texas A&M University System; Texas A&M University College Station
  摘要：The main result in this paper is motivated by the M,zard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random -sat model at positive temperature. Using the fact that one can safely assume the validity of the Ghirlanda-Guerra identities in these models, we prove hierarchical exchangeability of pure states for the asymptotic Gibbs measures, which allows us to apply a representation result for hierarchicall...
• 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...
• 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...
• 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 ...
• Bounded size bias coupling: a Gamma function bound, and universal Dickman-function behavior AI翻译
  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...