Probability Theory and Related Fields

最新文章

• 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
• Parabolic type equations associated with the Dirichlet form on the Sierpinski gasket AI翻译
  作者：Liu, Xuan; Qian, Zhongmin
  作者单位：University of Oxford
  摘要：By using analytic tools from stochastic analysis, we initiate a study of some non-linear parabolic equations on Sierpinski gasket, motivated by modellings of fluid flows along fractals (which can be considered as models of simplified rough porous media). Unlike the regular space case, such parabolic type equations involving non-linear convection terms must take a different form, due to the fact that convection terms must be singular to the linear part which defines the heat semigroup. In order...
• Cut-off phenomenon for random walks on free orthogonal quantum groups AI翻译
  作者：Freslon, Amaury
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
  摘要：We give bounds in total variation distance for random walks associated to pure central states on free orthogonal quantum groups. As a consequence, we prove that the analogue of the uniform plane Kac walk on this quantum group has a cut-off at Nln(N)/2(1-cos(theta)). This is the first result of this type for genuine compact quantum groups. We also obtain similar results for mixtures of rotations and quantum permutations.
• How long does it take for Internal DLA to forget its initial profile? AI翻译
  作者：Levine, Lionel; Silvestri, Vittoria
  作者单位：Cornell University; University of Cambridge
  摘要：Internal DLA is a discrete model of a moving interface. On the cylinder graph ZNxZ, a particle starts uniformly on ZNx{0} and performs simple random walk on the cylinder until reaching an unoccupied site in ZNxZ >= 0, which it occupies forever. This operation defines a Markov chain on subsets of the cylinder. We first show that a typical subset is rectangular with at most logarithmic fluctuations. We use this to prove that two Internal DLA chains started from different typical subsets can be c...
• A second order equation for Schrodinger bridges with applications to the hot gas experiment and entropic transportation cost AI翻译
  作者：Conforti, Giovanni
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：The Schrodinger problem is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schrodinger as the problem of describing the most likely evolution of a large number of Brownian particles conditioned to reach an unexpected configuration. Its optimal value, the entropic transportation cost, and its optimal solution, the Schrodinger bridge, stand as the natural probabilistic counterparts to the transportation cost and...
• The parabolic Anderson model on Riemann surfaces AI翻译
  作者：Dahlqvist, Antoine; Diehl, Joscha; Driver, Bruce K.
  作者单位：University College Dublin; Max Planck Society; University of California System; University of California San Diego
  摘要：We show well-posedness for the parabolic Anderson model on 2-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for this equation. A central ingredient is the appropriate re-interpretation of the polynomial model, which we build up to any order.
• The smallest singular value of a shifted d-regular random square matrix AI翻译
  作者：Litvak, Alexander E.; Lytova, Anna; Tikhomirov, Konstantin; Tomczak-Jaegermann, Nicole; Youssef, Pierre
  作者单位：University of Alberta; University of Opole; Princeton University; Universite Paris Cite
  摘要：We derive a lower bound on the smallest singular value of a random d-regular matrix, that is, the adjacency matrix of a random d-regular directed graph. Specifically, let C1
• Asymptotics of even-even correlations in the Ising model AI翻译
  作者：Ott, Sebastien; Velenik, Yvan
  作者单位：University of Geneva
  摘要：We consider finite-range ferromagnetic Ising models on Z(d) in the regime beta < beta(c). We analyze the behavior of the prefactor to the exponential decay of Cov(sigma(A), sigma(B)), for arbitrary finite sets A and B of even cardinality, as the distance between A and B diverges.
• Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model AI翻译
  作者：Merkl, Franz; Rolles, Silke W. W.; Tarres, Pierre
  作者单位：University of Munich; Technical University of Munich; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
  摘要：In this paper, we define an extension of the supersymmetric hyperbolic nonlinear sigma model introduced by Zirnbauer. We show that it arises as a weak joint limit of a time-changed version introduced by Sabot and Tarres of the vertex-reinforced jump process. It describes the asymptotics of rescaled crossing numbers, rescaled fluctuations of local times, asymptotic local times on a logarithmic scale, endpoints of paths, and last exit trees.