Probability Surveys最新文献_第4页

Time-uniform Chernoff bounds via nonnegative supermartingales 非负上鞅的时一致Chernoff界

IF 1.6

Probability Surveys Pub Date : 2018-08-09 DOI: 10.1214/18-ps321

Steven R. Howard, Aaditya Ramdas, Jon D. McAuliffe, J. Sekhon

引用次数: 115

Metastable Markov chains 亚稳态马尔可夫链

IF 1.6

Probability Surveys Pub Date : 2018-07-11 DOI: 10.1214/18-PS310

C. Landim

引用次数: 11

Equivalences and counterexamples between several definitions of the uniform large deviations principle 均匀大偏差原理若干定义的等价和反例

IF 1.6

Probability Surveys Pub Date : 2017-12-19 DOI: 10.1214/18-PS309

M. Salins

引用次数: 13

Limits of random tree-like discrete structures 随机树状离散结构的极限

IF 1.6

Probability Surveys Pub Date : 2016-12-08 DOI: 10.1214/19-ps338

Benedikt Stufler

{"title":"Limits of random tree-like discrete structures","authors":"Benedikt Stufler","doi":"10.1214/19-ps338","DOIUrl":"https://doi.org/10.1214/19-ps338","url":null,"abstract":"We study a model of random $mathcal{R}$-enriched trees that is based on weights on the $mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits describing local convergence around fixed and random points in this general context, limit theorems for component sizes when $mathcal{R}$ is a composite class, and a Gromov--Hausdorff scaling limit of random metric spaces patched together from independently drawn metrics on the $mathcal{R}$-structures. Our main applications treat a selection of examples encompassed by this model. We consider random outerplanar maps sampled according to arbitrary weights assigned to their inner faces, and classify in complete generality distributional limits for both the asymptotic local behaviour near the root-edge and near a uniformly at random drawn vertex. We consider random connected graphs drawn according to weights assigned to their blocks and establish a Benjamini--Schramm limit. We also apply our framework to recover in a probabilistic way a central limit theorem for the size of the largest $2$-connected component in random graphs from planar-like classes. We prove Benjamini--Schramm convergence of random $k$-dimensional trees and establish both scaling limits and local weak limits for random planar maps drawn according to Boltzmann-weights assigned to their $2$-connected components.","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2016-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66079960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 35

The Bethe ansatz for the six-vertex and XXZ models: An exposition 六顶点和XXZ模型的Bethe分析:阐述

IF 1.6

Probability Surveys Pub Date : 2016-11-29 DOI: 10.1214/17-PS292

H. Duminil-Copin, Maxime Gagnebin, Matan Harel, I. Manolescu, V. Tassion

{"title":"The Bethe ansatz for the six-vertex and XXZ models: An exposition","authors":"H. Duminil-Copin, Maxime Gagnebin, Matan Harel, I. Manolescu, V. Tassion","doi":"10.1214/17-PS292","DOIUrl":"https://doi.org/10.1214/17-PS292","url":null,"abstract":"In this paper, we review a few known facts on the coordinate Bethe ansatz. We present a detailed construction of the Bethe ansatz vector (psi) and energy (Lambda), which satisfy (V psi = Lambda psi), where (V) is the transfer matrix of the six-vertex model on a finite square lattice with periodic boundary conditions for weights (a= b=1) and (c > 0). We also show that the same vector (psi) satisfies (H psi = E psi), where (H) is the Hamiltonian of the XXZ model (which is the model for which the Bethe ansatz was first developed), with a value (E) computed explicitly. \u0000 \u0000Variants of this approach have become central techniques for the study of exactly solvable statistical mechanics models in both the physics and mathematics communities. Our aim in this paper is to provide a \u0000pedagogically-minded exposition of this construction, aimed at a mathematical audience. It also provides the opportunity to introduce the notation and framework which will be used in a subsequent paper by the authors [5] that amounts to proving that the random-cluster model on (mathbb{Z}^{2}) with cluster weight (q >4) exhibits a first-order phase transition. \u0000 \u0000","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2016-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/17-PS292","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66071434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 22

Equidistribution, uniform distribution: a probabilist's perspective 均衡分布，均匀分布:一个概率学家的观点

IF 1.6

Probability Surveys Pub Date : 2016-10-07 DOI: 10.1214/17-PS295

V. Limic, Nedvzad Limi'c

{"title":"Equidistribution, uniform distribution: a probabilist's perspective","authors":"V. Limic, Nedvzad Limi'c","doi":"10.1214/17-PS295","DOIUrl":"https://doi.org/10.1214/17-PS295","url":null,"abstract":"The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounter difficulties perusing the literature, due to various synonyms and polysemes used by different schools. One purpose of this note is to provide a short introduction for probabilists. We proceed by recalling a perspective originating in a work of the second author from 2002. Using it, various new examples of completely uniformly distributed (mathsf{mod}~1) sequences, in the “metric” (meaning almost sure stochastic) sense, can be easily exhibited. In particular, we point out natural generalizations of the original (p)-multiply equidistributed sequence (k^p, t {mathsf{mod}}~1), (kgeq1) (where (pinmathbb{N}) and (tin[0,1])), due to Hermann Weyl in 1916. In passing, we also derive a Weyl-like criterion for weakly completely equidistributed (also known as WCUD) sequences, of substantial recent interest in MCMC simulations. \u0000 \u0000The translation from number theory to probability language brings into focus a version of the strong law of large numbers for weakly correlated complex-valued random variables, the study of which was initiated by Weyl in the aforementioned manuscript, followed up by Davenport, Erdős and LeVeque in 1963, and greatly extended by Russell Lyons in 1988. In this context, an application to (infty)-distributed Koksma's numbers (t^k {mathsf{mod}}~1), (kgeq1) (where (tin[1,a]) for some (a>1)), and an important generalization by Niederreiter and Tichy from 1985 are discussed. \u0000 \u0000The paper contains negligible amount of new mathematics in the strict sense, but its perspective and open questions included in the end could be of considerable interest to probabilists and statisticians, as well as \u0000certain computer scientists and number theorists. \u0000 \u0000","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2016-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66071523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

On the scaling limits of weakly asymmetric bridges 弱不对称桥梁的标度极限

IF 1.6

Probability Surveys Pub Date : 2016-09-19 DOI: 10.1214/17-PS285

C. Labb'e

引用次数: 7

TASEP hydrodynamics using microscopic characteristics TASEP流体力学的微观特征

IF 1.6

Probability Surveys Pub Date : 2016-01-20 DOI: 10.1214/17-PS284

P. Ferrari

引用次数: 15

From extreme values of i.i.d. random fields to extreme eigenvalues of finite-volume Anderson Hamiltonian 从i.i.d随机场的极值到有限体积安德森哈密顿算子的极值特征值

IF 1.6

Probability Surveys Pub Date : 2015-01-05 DOI: 10.1214/15-PS252

A. Astrauskas

{"title":"From extreme values of i.i.d. random fields to extreme eigenvalues of finite-volume Anderson Hamiltonian","authors":"A. Astrauskas","doi":"10.1214/15-PS252","DOIUrl":"https://doi.org/10.1214/15-PS252","url":null,"abstract":"The aim of this paper is to study asymptotic geometric properties \u0000almost surely or/and in probability of extreme order statistics of an \u0000i.i.d. random field (potential) indexed by sites of multidimensional lattice \u0000cube, the volume of which unboundedly increases. We discuss the following \u0000topics: (I) high level exceedances, in particular, clustering of exceedances; \u0000(II) decay rate of spacings in comparison with increasing rate of extreme order \u0000statistics; (III) minimum of spacings of successive order statistics; (IV) \u0000asymptotic behavior of values neighboring to extremes and so on. The conditions \u0000of the results are formulated in terms of regular variation (RV) of \u0000the cumulative hazard function and its inverse. A relationship between RV \u0000classes of the present paper as well as their links to the well-known RV \u0000classes (including domains of attraction of max-stable distributions) are \u0000discussed. \u0000The asymptotic behavior of functionals (I)–(IV) determines the asymptotic \u0000structure of the top eigenvalues and the corresponding eigenfunctions \u0000of the large-volume discrete Schrodinger operators with an i.i.d. potential \u0000(Anderson Hamiltonian). Thus, another aim of the present paper is \u0000to review and comment a recent progress on the extreme value theory for \u0000eigenvalues of random Schrodinger operators as well as to provide a clear \u0000and rigorous understanding of the relationship between the top eigenvalues \u0000and extreme values of i.i.d. random potentials. We also discuss their links \u0000to the long-time intermittent behavior of the parabolic problems associated \u0000with the Anderson Hamiltonian via spectral representation of solutions.","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2015-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/15-PS252","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66046450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 26

Current open questions in complete mixability 目前开放的问题在完全混合

IF 1.6

Probability Surveys Pub Date : 2014-11-23 DOI: 10.1214/14-PS250

Ruodu Wang

引用次数: 11