Probability Theory and Related Fields

最新文章

• The probability of intransitivity in dice and close elections AI翻译
  作者：Hazla, Jan; Mossel, Elchanan; Ross, Nathan; Zheng, Guangqu
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Massachusetts Institute of Technology (MIT); University of Melbourne; University of Kansas
  摘要：We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We build on a recent result of Polymath showing that three dice with i.i.d. faces drawn from the uniform distribution on {1, ... , n} and conditioned on the average of faces equal to (n+1)/2 are intransitive with asymptotic probability 1/4. We ...
• Outliers of random perturbations of Toeplitz matrices with finite symbols AI翻译
  作者：Basak, Anirban; Zeitouni, Ofer
  作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; Weizmann Institute of Science; New York University
  摘要：Consider an N x N Toeplitz matrix T-N with symbol a(lambda) := Sigma(d1)(l=-d2) a(e)lambda(e), perturbed by an additive noise matrix N-gamma E-N, where the entries of E-N are centered i.i.d. random variables of unit variance and gamma > 1/2. It is known that the empirical measure of eigenvalues of the perturbed matrix converges weakly, as N -> infinity, to the law of a(U), where U is distributed uniformly on S-1. In this paper, we consider the outliers, i.e. eigenvalues that are at a positive ...
• Algorithmic Pirogov-Sinai theory AI翻译
  作者：Helmuth, Tyler; Perkins, Will; Regts, Guus
  作者单位：University of Bristol; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Amsterdam
  摘要：We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice Zd and on the torus (Z/nZ)d. Our approach is based on combining contour representations from Pirogov-Sinai theory with Barvinok's approach to approximate counting using truncated Taylor series. Some consequences of our main results include an FPTAS for approximating the partition function of the hard-cor...
• Dyson Brownianmotion for general β and potential at the edge AI翻译
  作者：Adhikari, Arka; Huang, Jiaoyang
  作者单位：Harvard University
  摘要：In this paper, we compare the solutions of the Dyson Brownian motion for general beta and potential V and the associated McKean-Vlasov equation near the edge. Under suitable conditions on the initial data and the potential V, we obtain optimal rigidity estimates of particle locations near the edge after a short time t = o(1). Our argument uses the method of characteristics along with a careful estimate involving an equation of the edge. With the rigidity estimates as an input, we prove a centr...
• The mean field Schrodinger problem: ergodic behavior, entropy estimates and functional inequalities AI翻译
  作者：Backhoff, Julio; Conforti, Giovani; Gentil, Ivan; Leonard, Christian
  作者单位：University of Vienna; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Twente
  摘要：We study the mean field Schrodinger problem (MFSP), that is the problem of finding the most likely evolution of a cloud ofinteractingBrownian particles conditionally on the observation of their initial and final configuration. Its rigorous formulation is in terms of an optimization problem with marginal constraints whose objective function is the large deviation rate function associated with a system of weakly dependent Brownian particles. We undertake a fine study of the dynamics of its solut...
• Robust statistical learning with Lipschitz and convex loss functions AI翻译
  作者：Chinot, Geoffrey; Lecue, Guillaume; Lerasle, Matthieu
  摘要：We obtain estimation and excess risk bounds for Empirical Risk Minimizers (ERM) and minmax Median-Of-Means (MOM) estimators based on loss functions that are both Lipschitz and convex. Results for the ERM are derived under weak assumptions on the outputs and subgaussian assumptions on the design as in Alquier et al. (Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functions. arXiv:1702.01402, 2017). The difference with Alquier et al. (2017) is that ...
• Zero-temperature Glauber dynamics on the 3-regular tree and the median process AI翻译
  作者：Damron, Michael; Sen, Arnab
  作者单位：University System of Georgia; Georgia Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities
  摘要：In zero-temperature Glauber dynamics, vertices of a graph are given i.i.d. initial spins sigma(x) (0) from {-1,+1} with P-p(sigma(x) (0) = +1) = p, and they update their spins at the arrival times of i.i.d. Poisson processes to agree with a majority of their neighbors. We study this process on the 3-regular tree T-3, where it is known that the critical threshold p(c), below which Pp-a.s. all spins fixate to -1, is strictly less than 1/2. Defining theta(p) to be the P-p-probability that a verte...
• Geometry of the random walk range conditioned on survival among Bernoulli obstacles AI翻译
  作者：Ding, Jian; Fukushima, Ryoki; Sun, Rongfeng; Xu, Changji
  作者单位：University of Pennsylvania; Kyoto University; National University of Singapore; University of Chicago
  摘要：We consider a discrete time simple symmetric random walk among Bernoulli obstacles on Z(d), d >= 2, where the walk is killed when it hits an obstacle. It is known that conditioned on survival up to time N, the random walk range is asymptotically contained in a ball of radius (sic)N = CN1/(d+ 2) for any d = 2. For d = 2, it is also known that the range asymptotically contains a ball of radius (1-) N for any > 0, while the case d = 3 remains open. We complete the picture by showing that for any ...
• Infinite-dimensional stochastic differential equations and tail σ-fields AI翻译
  作者：Osada, Hirofumi; Tanemura, Hideki
  作者单位：Kyushu University; Keio University
  摘要：We present general theorems solving the long-standing problem of the existence and pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential equations (ISDEs) called interacting Brownian motions. These ISDEs describe the dynamics of infinitely-many Brownian particles moving in R-d with free potential Phi and mutual interaction potential Psi. We apply the theorems to essentially all interaction potentials of Ruelle's class such as the Lennard-Jones 6-12 potential a...
• The geometry of multi-marginal Skorokhod Embedding AI翻译
  作者：Beiglboeck, Mathias; Cox, Alexander M. G.; Huesmann, Martin
  作者单位：University of Vienna; University of Bath
  摘要：The Skorokhod Embedding Problem is one of the classical problems in the theory of stochastic processes, with applications in many different fields [cf. the surveys (Hobson in: Paris-Princeton lectures on mathematical finance 2010, Volume 2003 of Lecture Notes in Mathematics, Springer, Berlin, 2011; Oboj in: Probab Surv 1:321-390, 2004)]. Many of these applications have natural multi-marginal extensions leading to the (optimal) multi-marginal Skorokhod problem. Some of the first papers to consi...