Probability Theory and Related Fields

最新文章

• Shotgun assembly threshold for lattice labeling model AI翻译
  作者：Ding, Jian; Liu, Haoyu
  作者单位：Peking University
  摘要：We study the shotgun assembly problem for the lattice labeling model, where i.i.d. uniform labels are assigned to each vertex in a d-dimensional box of side length n. We wish to recover the labeling configuration on the whole box given empirical profile of labeling configurations on all boxes of side length r. We determine the threshold around which there is a sharp transition from impossible to recover with probability tending to 1, to possible to recover with an efficient algorithm with prob...
• Sharp uniform-in-time propagation of chaos AI翻译
  作者：Lacker, Daniel; Le Flem, Luc
  作者单位：Columbia University
  摘要：We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions. Our main examples are interactions governed by convex potentials and models on the torus with small interactions. We show that the distance between the k-particle marginal of the n-particle system and its limiting product measure is O((k/n)(2)), uniformly in time, with distance measured either by relative entropy, squared quadratic Wasserstein metric, or squared total variation. Our p...
• Universal cutoff for Dyson Ornstein Uhlenbeck process AI翻译
  作者：Boursier, Jeanne; Chafai, Djalil; Labbe, Cyril
  作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite
  摘要：We study the Dyson-Ornstein-Uhlenbeck diffusion process, an evolving gas of interacting particles. Its invariant law is the beta Hermite ensemble of random matrix theory, a non-product log-concave distribution. We explore the convergence to equilibrium of this process for various distances or divergences, including total variation, relative entropy, and transportation cost. When the number of particles is sent to infinity, we show that a cutoff phenomenon occurs: the distance to equilibrium va...
• CLT in functional linear regression models (vol 138, 325, 2007) AI翻译
  作者：Cardot, Herve; Mas, Andre; Sarda, Pascal
  作者单位：Institut Agro; AgroSup Dijon; Universite de Montpellier; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Universite de Toulouse - Jean Jaures
• Random walks on SL2(C): spectral gap and limit theorems AI翻译
  作者：Dinh, Tien-Cuong; Kaufmann, Lucas; Wu, Hao
  作者单位：National University of Singapore; Institute for Basic Science - Korea (IBS); Centre National de la Recherche Scientifique (CNRS); Universite de Orleans
  摘要：We obtain various new limit theorems for random walks on SL2(C) under low moment conditions. For non-elementary measures with a finite second moment we prove a Local Limit Theorem for the norm cocycle, yielding the optimal version of a theorem of E. Le Page. For measures with a finite third moment, we obtain the Local Limit Theorem for the matrix coefficients, improving a recent result of Grama-Quint-Xiao and the authors, and Berry-Esseen bounds with optimal rate O(1/root n) for the norm cocyc...
• Estimating the probability that a given vector is in the convex hull of a random sample AI翻译
  作者：Hayakawa, Satoshi; Lyons, Terry; Oberhauser, Harald
  作者单位：University of Oxford
  摘要：For a d-dimensional random vector X, let p(n,X)(theta) be the probability that the convex hull of n independent copies of X contains a given point theta. We provide several sharp inequalities regarding p(n,X)(theta) and N-X(theta) denoting the smallest n for which p(n,X)(theta) >= 1/2. As a main result, we derive the totally general inequality 1/2 <= alpha(X)(theta)N-X(theta) <= 3d + 1, where alpha(X)(theta) (a.k.a. the Tukey depth) is the minimum probability that X is in a fixed closed halfsp...
• Exact value of the resistance exponent for four dimensional random walk trace (vol 153, pg 191, 2012) AI翻译
  作者：Croydon, D. A.; Shiraishi, D.
  作者单位：Kyoto University
  摘要：We correct a proof in the article 'D. Shiraishi, Exact value of the resistance exponent for four dimensional random walk trace, Probab. Theory and Related Fields 153 (2012), no. 1-2, 191-232'.
• Cut-off phenomenon for the ax plus b Markov chain over a finite field AI翻译
  作者：Breuillard, Emmanuel; Varju, Peter P.
  作者单位：University of Oxford; University of Cambridge
  摘要：We study the Markov chain x(n+1 )= ax(n) + b(n) on a finite field F-p, where a is an element of F-p(x) is fixed and b(n) are independent and identically distributed random variables in F-p. Conditionally on the Riemann hypothesis for all Dedekind zeta functions, we show that the chain exhibits a cut-off phenomenon for most primes p and most values of a is an element of F-p(x). We also obtain weaker, but unconditional, upper bounds for the mixing time.
• Absolute continuity and singularity of Palm measures of the Ginibre point process (vol 165, pg 725, 2016) AI翻译
  作者：Osada, Hirofumi; Shirai, Tomoyuki
  作者单位：Kyushu University; Kyushu University
• Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model AI翻译
  作者：Korotkikh, Sergei
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：We study a new integrable probabilistic system, defined in terms of a stochastic colored vertex model on a square lattice. The main distinctive feature of our model is a new family of parameters attached to diagonals rather than to rows or columns, like in other similar models. Because of these new parameters the previously known results about vertex models cannot be directly applied, but nevertheless the integrability remains, and we prove explicit integral expressions for q-deformed moments ...