Annals of Probability最新文献

Decay of convolved densities via Laplace transform 卷积密度的拉普拉斯变换衰减

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1625

Sergey G. Bobkov

引用次数: 0

Convergence and nonconvergence of scaled self-interacting random walks to Brownian motion perturbed at extrema 尺度自相互作用随机漫步到极值摄动布朗运动的收敛性与非收敛性

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1629

Elena Kosygina, Thomas Mountford, Jonathon Peterson

{"title":"Convergence and nonconvergence of scaled self-interacting random walks to Brownian motion perturbed at extrema","authors":"Elena Kosygina, Thomas Mountford, Jonathon Peterson","doi":"10.1214/23-aop1629","DOIUrl":"https://doi.org/10.1214/23-aop1629","url":null,"abstract":"We use generalized Ray–Knight theorems, introduced by B. Tóth in 1996, together with techniques developed for excited random walks as main tools for establishing positive and negative results concerning convergence of some classes of diffusively scaled self-interacting random walks (SIRW) to Brownian motions perturbed at extrema (BMPE). Tóth’s work studied two classes of SIRWs: asymptotically free and polynomially self-repelling walks. For both classes Tóth has shown, in particular, that the distribution function of a scaled SIRW observed at independent geometric times converges to that of a BMPE indicated by the generalized Ray–Knight theorem for this SIRW. The question of weak convergence of one-dimensional distributions of scaled SIRW remained open. In this paper, on the one hand, we prove a full functional limit theorem for a large class of asymptotically free SIRWs, which includes the asymptotically free walks considered by Tóth. On the other hand, we show that rescaled polynomially self-repelling SIRWs do not converge to the BMPE predicted by the corresponding generalized Ray–Knight theorems and hence do not converge to any BMPE.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135305461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global information from local observations of the noisy voter model on a graph 全局信息来自局部观测的有噪声选民模型上的一个图

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1637

Itai Benjamini, Hagai Helman Tov, Maksim Zhukovskii

引用次数: 1

Perturbations of parabolic equations and diffusion processes with degeneration: Boundary problems, metastability, and homogenization 带退化的抛物方程和扩散过程的扰动:边界问题、亚稳态和均匀化

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1631

Mark Freidlin, Leonid Koralov

引用次数: 0

The phase transition for planar Gaussian percolation models without FKG 无FKG时平面高斯渗流模型的相变

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1633

Stephen Muirhead, Alejandro Rivera, Hugo Vanneuville, Laurin Köhler-Schindler

{"title":"The phase transition for planar Gaussian percolation models without FKG","authors":"Stephen Muirhead, Alejandro Rivera, Hugo Vanneuville, Laurin Köhler-Schindler","doi":"10.1214/23-aop1633","DOIUrl":"https://doi.org/10.1214/23-aop1633","url":null,"abstract":"We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These models lack the property of positive associations (also known as the ‘FKG inequality’), and hence many classical arguments in percolation theory do not apply. More precisely, we consider a smooth stationary centred planar Gaussian field f and, given a level ℓ∈R, we study the connectivity properties of the excursion set {f≥−ℓ}. We prove the existence of a phase transition at the critical level ℓcrit=0 under only symmetry and (very mild) correlation decay assumptions, which are satisfied by the random plane wave for instance. As a consequence, all nonzero level lines are bounded almost surely, although our result does not settle the boundedness of zero level lines (‘no percolation at criticality’). To show our main result: (i) we prove a general sharp threshold criterion, inspired by works of Chatterjee, that states that ‘sharp thresholds are equivalent to the delocalisation of the threshold location’; (ii) we prove threshold delocalisation for crossing events at large scales—at this step we obtain a sharp threshold result but without being able to locate the threshold—and (iii) to identify the threshold, we adapt Tassion’s RSW theory replacing the FKG inequality by a sprinkling procedure. Although some arguments are specific to the Gaussian setting, many steps are very general and we hope that our techniques may be adapted to analyse other models without FKG.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135636424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

Stationary measures for the log-gamma polymer and KPZ equation in half-space 半空间中对数聚合物的稳态测量和KPZ方程

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1634

Guillaume Barraquand, Ivan Corwin

引用次数: 13

Most transient random walks have infinitely many cut times 大多数瞬态随机漫步具有无限多的切割时间

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1636

Noah Halberstam, Tom Hutchcroft

引用次数: 0

Scaling limit of the heavy tailed ballistic deposition model with p-sticking p-粘滞重尾弹道沉积模型的结垢极限

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1635

Francis Comets, Joseba Dalmau, Santiago Saglietti

引用次数: 2

Universality of approximate message passing with semirandom matrices 半随机矩阵近似消息传递的通用性

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1628

Rishabh Dudeja, Yue M. Lu, Subhabrata Sen

{"title":"Universality of approximate message passing with semirandom matrices","authors":"Rishabh Dudeja, Yue M. Lu, Subhabrata Sen","doi":"10.1214/23-aop1628","DOIUrl":"https://doi.org/10.1214/23-aop1628","url":null,"abstract":"Approximate Message Passing (AMP) is a class of iterative algorithms that have found applications in many problems in high-dimensional statistics and machine learning. In its general form, AMP can be formulated as an iterative procedure driven by a matrix M. Theoretical analyses of AMP typically assume strong distributional properties on M, such as M has i.i.d. sub-Gaussian entries or is drawn from a rotational invariant ensemble. However, numerical experiments suggest that the behavior of AMP is universal as long as the eigenvectors of M are generic. In this paper we take the first step in rigorously understanding this universality phenomenon. In particular, we investigate a class of memory-free AMP algorithms (proposed by Çakmak and Opper for mean-field Ising spin glasses) and show that their asymptotic dynamics is universal on a broad class of semirandom matrices. In addition to having the standard rotational invariant ensemble as a special case, the class of semirandom matrices that we define in this work also includes matrices constructed with very limited randomness. One such example is a randomly signed version of the sine model, introduced by Marinari, Parisi, Potters, and Ritort for spin glasses with fully deterministic couplings.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135305470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

On strong solutions of Itô’s equations with Dσ and b in Morrey classes containing Ld 含Ld的Morrey类中含有Dσ和b的Itô方程的强解

1区数学

Annals of Probability Pub Date : 2023-09-01 DOI: 10.1214/23-aop1630

N.V. Krylov

引用次数: 4