3-4期

最新文章

• The local limit theorem on nilpotent Lie groups AI翻译
  作者：Hough, Robert
  作者单位：State University of New York (SUNY) System; Stony Brook University
  摘要：A local limit theorem is proven on connected, simply connected nilpotent Lie groups, for a class of generating measures satisfying a moment condition and a condition on the characteristic function of the abelianization. The result extends an earlier local limit theorem of Alexopoulos which treated absolutely continuous measures with a continuous density of compact support, and also extends local limit theorems of Breuillard and Diaconis-Hough which treated general measures on the Heisenberg gr...
• A distance exponent for Liouville quantum gravity AI翻译
  作者：Gwynne, Ewain; Holden, Nina; Sun, Xin
  作者单位：Massachusetts Institute of Technology (MIT); Columbia University
  摘要：Let (0,2) and let h be the random distribution on C which describes a -Liouville quantum gravity (LQG) cone. Also let =16/2>4 and let be a whole-plane space-filling SLE curve sampled independent from h and parametrized by -quantum mass with respect to h. We study a family {GE}E>0 of planar maps associated with (h,) called the LQG structure graphs (a.k.a. mated-CRT maps) which we conjecture converge in probability in the scaling limit with respect to the Gromov-Hausdorff topology to a random me...
• Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement AI翻译
  作者：Nestoridi, Evita
  作者单位：Princeton University
  摘要：This paper studies Markov chains on the chambers of real hyperplane arrangements, a model that generalizes famous examples, such as the Tsetlin library and riffle shuffles. We discuss cutoff for the Tsetlin library for general weights, and we give an exact formula for the separation distance for the hyperplane arrangement walk. We introduce lower bounds, which allow for the first time to study cutoff for hyperplane arrangement walks under certain conditions. Using similar techniques, we also p...
• Random walks of infinite moment on free semigroups AI翻译
  作者：Forghani, Behrang; Tiozzo, Giulio
  作者单位：Bowdoin College; University of Toronto
  摘要：We consider random walks on finitely or countably generated free semigroups, and identify their Poisson boundaries for classes of measures which fail to meet the classical entropy criteria, namely measures with infinite entropy or infinite logarithmic moment.
• The two-time distribution in geometric last-passage percolation AI翻译
  作者：Johansson, Kurt
  作者单位：Royal Institute of Technology
  摘要：We study the two-time distribution in directed last passage percolation with geometric weights in the first quadrant. We compute the scaling limit and show that it is given by a contour integral of a Fredholm determinant.
• Local limits of lozenge tilings are stable under bounded boundary height perturbations AI翻译
  作者：Laslier, Benoit
  作者单位：Universite Paris Cite
  摘要：We show that bounded changes to the boundary of a lozenge tilings do not affect the local behaviour inside the domain. As a consequence we prove the existence of a local limit in all domains with planar boundary. The proof does not rely on any exact solvability of the model beyond its links with uniform spanning trees.
• Near-optimal mean estimators with respect to general norms AI翻译
  作者：Lugosi, Gabor; Mendelson, Shahar
  作者单位：Pompeu Fabra University; ICREA; Universite Paris Cite; Sorbonne Universite; Australian National University
  摘要：We study the problem of estimating the mean of a random vector in based on an i.i.d. sample, when the accuracy of the estimator is measured by a general norm on . We construct an estimator (that depends on the norm) that achieves an essentially optimal accuracy/confidence tradeoff under the only assumption that the random vector has a well-defined covariance matrix. At the heart of the argument is the construction of a uniform median-of-means estimator in a class of real valued functions.
• Super-Ricci flows and improved gradient and transport estimates AI翻译
  作者：Kopfer, Eva
  作者单位：University of Bonn
  摘要：We introduce Brownian motions on time-dependent metric measure spaces, proving their existence and uniqueness. We prove contraction estimates for their trajectories assuming that the time-dependent heat flow satisfies transport estimates with respect to every L-p-Kantorovich distance, p. [1,8]. These transport estimates turn out to characterize super-Ricci flows, introduced by Sturm (J Funct Anal 275(12):3504-3569, 2015.)
• Rigidity of the three-dimensional hierarchical Coulomb gas AI翻译
  作者：Chatterjee, Sourav
  作者单位：Stanford University
  摘要：A random set of points in Euclidean space is called 'rigid' or 'hyperuniform' if the number of points falling inside any given region has significantly smaller fluctuations than the corresponding number for a set of i.i.d. random points. This phenomenon has received considerable attention in recent years, due to its appearance in random matrix theory, the theory of Coulomb gases and zeros of random analytic functions. However, most of the published results are in dimensions one and two. This p...
• The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference AI翻译
  作者：Barbier, Jean; Macris, Nicolas
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Abdus Salam International Centre for Theoretical Physics (ICTP)
  摘要：In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or free energy) in Bayesian inference problems. The proof techniques that have emerged appear to be quite general, despite they have been worked out on a case-by-case basis. Unfortunately, a common point between all these schemes is their relatively high level of technicality. We present a new proof scheme that is quite straightforward with respe...