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Scaling limit for line ensembles of random walks with geometric area tilts 具有几何面积倾斜的随机漫步线集合的尺度限制
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1026
Christian Serio
{"title":"Scaling limit for line ensembles of random walks with geometric area tilts","authors":"Christian Serio","doi":"10.1214/23-ejp1026","DOIUrl":"https://doi.org/10.1214/23-ejp1026","url":null,"abstract":"We consider line ensembles of non-intersecting random walks constrained by a hard wall, each tilted by the area underneath it with geometrically growing pre-factors bi where b>1. This is a model for the level lines of the (2+1)D SOS model above a hard wall, which itself mimics the low-temperature 3D Ising interface. A similar model with b=1 and a fixed number of curves was studied by Ioffe, Velenik, and Wachtel (2018), who derived a scaling limit as the time interval [−N,N] tends to infinity. Line ensembles of Brownian bridges with geometric area tilts (b>1) were studied by Caputo, Ioffe, and Wachtel (2019), and later by Dembo, Lubetzky, and Zeitouni (2022+). Their results show that as the time interval and the number of curves n tend to infinity, the top k paths converge to a limiting measure μ. In this paper we address the open problem of proving existence of a scaling limit for random walk ensembles with geometric area tilts. We prove that with mild assumptions on the jump distribution, under suitable scaling the top k paths converge to the same measure μ as N→∞ followed by n→∞. We do so both in the case of bridges fixed at ±N and of walks fixed only at −N.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135261330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3
Exponential asymptotics for Brownian self-intersection local times under Dalang’s condition Dalang条件下布朗自交局部时的指数渐近性
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp985
Xia Chen
{"title":"Exponential asymptotics for Brownian self-intersection local times under Dalang’s condition","authors":"Xia Chen","doi":"10.1214/23-ejp985","DOIUrl":"https://doi.org/10.1214/23-ejp985","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Regularisation by fractional noise for one-dimensional differential equations with distributional drift 具有分布漂移的一维微分方程的分数噪声正则化
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1010
Lukas Anzeletti, Alexandre Richard, Etienne Tanré
{"title":"Regularisation by fractional noise for one-dimensional differential equations with distributional drift","authors":"Lukas Anzeletti, Alexandre Richard, Etienne Tanré","doi":"10.1214/23-ejp1010","DOIUrl":"https://doi.org/10.1214/23-ejp1010","url":null,"abstract":"We study existence and uniqueness of solutions to the equation dXt=b(Xt)dt+dBt, where b is a distribution in some Besov space and B is a fractional Brownian motion with Hurst parameter H⩽1∕2. First, the equation is understood as a nonlinear Young equation. This involves a nonlinear Young integral constructed in the space of functions with finite p-variation, which is well suited when b is a measure. Depending on H, a condition on the Besov regularity of b is given so that solutions to the equation exist. The construction is deterministic, and B can be replaced by a deterministic path w with a sufficiently smooth local time. Using this construction we prove the existence of weak solutions (in the probabilistic sense). We also prove that solutions coincide with limits of strong solutions obtained by regularisation of b. This is used to establish pathwise uniqueness and existence of a strong solution. In particular when b is a finite measure, weak solutions exist for H< 2−1, while pathwise uniqueness and strong existence hold when H⩽1∕4. The proofs involve fine properties of the local time of the fractional Brownian motion, as well as new regularising properties of this process which are established using the stochastic sewing Lemma.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 8
Percolation in the Boolean model with convex grains in high dimension 高维凸粒布尔模型中的渗流
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp997
Jean-Baptiste Gouéré, Florestan Labéy
{"title":"Percolation in the Boolean model with convex grains in high dimension","authors":"Jean-Baptiste Gouéré, Florestan Labéy","doi":"10.1214/23-ejp997","DOIUrl":"https://doi.org/10.1214/23-ejp997","url":null,"abstract":"We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K⊂Rd with non empty interior. In a first setting, the Boolean model is a reunion of translates of K. In a second setting, the Boolean model is a reunion of translates of K or ρK for a further parameter ρ∈(1,2). We give the asymptotic behavior of the percolation probability and of the percolation threshold in the two settings.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Multi-dimensional BSDEs with mean reflection 具有平均反射的多维BSDEs
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp991
Baoyou Qu, Falei Wang
{"title":"Multi-dimensional BSDEs with mean reflection","authors":"Baoyou Qu, Falei Wang","doi":"10.1214/23-ejp991","DOIUrl":"https://doi.org/10.1214/23-ejp991","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47703775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Corrigendum to: The sum of powers of subtree sizes for conditioned Galton–Watson trees 勘误表：条件Galton–Watson树子树大小的幂和
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp915
J. A. Fill, S. Janson
{"title":"Corrigendum to: The sum of powers of subtree sizes for conditioned Galton–Watson trees","authors":"J. A. Fill, S. Janson","doi":"10.1214/23-ejp915","DOIUrl":"https://doi.org/10.1214/23-ejp915","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41592721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A sprinkled decoupling inequality for Gaussian processes and applications 高斯过程的离散解耦不等式及其应用
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp994
S. Muirhead
{"title":"A sprinkled decoupling inequality for Gaussian processes and applications","authors":"S. Muirhead","doi":"10.1214/23-ejp994","DOIUrl":"https://doi.org/10.1214/23-ejp994","url":null,"abstract":"We establish a sprinkled decoupling inequality for increasing events of Gaussian vectors with an error that depends only on the maximum pairwise correlation. As an application we prove the non-triviality of the percolation phase transition for Gaussian fields on $mathbb{Z}^d$ or $mathbb{R}^d$ with (i) uniformly bounded local suprema, and (ii) correlations which decay at least polylogarithmically in the distance with exponent $gamma>3$; this expands the scope of existing results on non-triviality of the phase transition, covering new examples such as non-stationary fields and monochromatic random waves.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46429317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Classification of stationary distributions for the stochastic vertex models 随机顶点模型的平稳分布分类
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1022
Yier Lin
{"title":"Classification of stationary distributions for the stochastic vertex models","authors":"Yier Lin","doi":"10.1214/23-ejp1022","DOIUrl":"https://doi.org/10.1214/23-ejp1022","url":null,"abstract":"In this paper, we study the stationary distributions for the stochastic vertex models. Our main focus is the stochastic six vertex (S6V) model. We show that the extremal stationary distributions of the S6V model are given by product Bernoulli measures. Moreover, for the S6V model under a moving frame of speed 1, we show that the extremal stationary distributions are given by product Bernoulli measures and blocking measures. Finally, we generalize our results to the stochastic higher spin six vertex model. Our proof relies on the coupling of the S6V models introduced in [4], the analysis of current and the method of fusion.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135261333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
On the free Lévy measure of the normal distribution 关于正态分布的自由lsm测度
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1035
Takahiro Hasebe, Yuki Ueda
{"title":"On the free Lévy measure of the normal distribution","authors":"Takahiro Hasebe, Yuki Ueda","doi":"10.1214/23-ejp1035","DOIUrl":"https://doi.org/10.1214/23-ejp1035","url":null,"abstract":"Belinschi et al. [Adv. Math., 226 (2011)] proved that the normal distribution is freely infinitely divisible. This paper establishes a certain monotonicity, real analyticity and asymptotic behavior of the density of the free Lévy measure. The monotonicity property strengthens the result in Hasebe et al. [Int. Math. Res. Not. (2019)] that the normal distribution is freely selfdecomposable.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Joint localization of directed polymers 定向聚合物的联合定位
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1000
Yurii Bakhtin, Douglas Dow
{"title":"Joint localization of directed polymers","authors":"Yurii Bakhtin, Douglas Dow","doi":"10.1214/23-ejp1000","DOIUrl":"https://doi.org/10.1214/23-ejp1000","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43196308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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