{"title":"A new three-dimensional extension of Bougerol’s identity in law","authors":"Kolitha Perera","doi":"10.1214/24-ecp577","DOIUrl":"https://doi.org/10.1214/24-ecp577","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140517595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotics of the rate function in the large deviation principle for sums of independent identically distributed random variables","authors":"I. Pinelis","doi":"10.1214/24-ecp584","DOIUrl":"https://doi.org/10.1214/24-ecp584","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140517286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonequilibrium moderate deviations from hydrodynamics of the simple symmetric exclusion process","authors":"Xiaofeng Xue","doi":"10.1214/24-ecp573","DOIUrl":"https://doi.org/10.1214/24-ecp573","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140516176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Let (Ω , F ) be a standard Borel space and P ( F ) the collection of all probability measures on F . Let E ⊂ Ω × Ω be a measurable equivalence relation, that is, E ∈ F⊗F and the relation on Ω defined as x ∼ y ⇔ ( x,y ) ∈ E is reflexive, symmetric and transitive. It is shown that there are two σ -fields G 0 and G 1 on Ω such that, for all µ, ν ∈ P ( F ),
.让 (Ω , F ) 是一个标准的 Borel 空间，P ( F ) 是 F 上所有概率度量的集合。让 E ⊂Ω × Ω 是可测等价关系，即 E∈F⊗F 和 Ω 上的关系定义为 x ∼ y ⇔ ( x,y ) ∈ E 是重外向、对称和传递的。证明在 Ω 上有两个 σ - 费尔德 G 0 和 G 1，对于所有 µ，ν ∈ P ( F ) 、
{"title":"Some duality results for equivalence couplings and total variation","authors":"L. Pratelli, P. Rigo","doi":"10.1214/24-ecp586","DOIUrl":"https://doi.org/10.1214/24-ecp586","url":null,"abstract":". Let (Ω , F ) be a standard Borel space and P ( F ) the collection of all probability measures on F . Let E ⊂ Ω × Ω be a measurable equivalence relation, that is, E ∈ F⊗F and the relation on Ω defined as x ∼ y ⇔ ( x,y ) ∈ E is reflexive, symmetric and transitive. It is shown that there are two σ -fields G 0 and G 1 on Ω such that, for all µ, ν ∈ P ( F ),","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140519377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Large deviations for the longest alternating and the longest increasing subsequence in a random permutation avoiding a pattern of length three","authors":"Ross G. Pinsky","doi":"10.1214/24-ecp579","DOIUrl":"https://doi.org/10.1214/24-ecp579","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140523384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joseph S. Alameda, Caroline Bang, Zachary Brennan, David P. Herzog, Jurgen Kritschgau, Elizabeth Sprangel
{"title":"Cutoff in the Bernoulli-Laplace urn model with swaps of order n","authors":"Joseph S. Alameda, Caroline Bang, Zachary Brennan, David P. Herzog, Jurgen Kritschgau, Elizabeth Sprangel","doi":"10.1214/23-ecp569","DOIUrl":"https://doi.org/10.1214/23-ecp569","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139458360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the spine of the two-particle Fleming-Viot process driven by Brownian motion","authors":"Krzysztof Burdzy, Tvrtko Tadi","doi":"10.1214/24-ecp581","DOIUrl":"https://doi.org/10.1214/24-ecp581","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140524245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extended Lévy’s theorem for a two-sided reflection","authors":"Benjamin Housley","doi":"10.1214/24-ecp576","DOIUrl":"https://doi.org/10.1214/24-ecp576","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140518937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the number of holes created by an “earthworm” moving on the two-dimensional integer lattice. The earthworm is modeled by a simple random walk. At the initial time, all vertices are filled with grains of soil except for the position of the earthworm. At each step, the earthworm pushes the soil in the direction of its motion. It leaves a hole (an empty vertex with no grain of soil) behind it. If there are holes in front of the earthworm (in the direction of its step), the closest hole is filled with a grain of soil. Thus the number of holes increases by 1 or remains unchanged at every step. We show that the number of holes is at least O(n3∕4)after n steps.
{"title":"On the size of earthworm’s trail","authors":"Krzysztof Burdzy, Shi Feng, Daisuke Shiraishi","doi":"10.1214/23-ecp556","DOIUrl":"https://doi.org/10.1214/23-ecp556","url":null,"abstract":"We investigate the number of holes created by an “earthworm” moving on the two-dimensional integer lattice. The earthworm is modeled by a simple random walk. At the initial time, all vertices are filled with grains of soil except for the position of the earthworm. At each step, the earthworm pushes the soil in the direction of its motion. It leaves a hole (an empty vertex with no grain of soil) behind it. If there are holes in front of the earthworm (in the direction of its step), the closest hole is filled with a grain of soil. Thus the number of holes increases by 1 or remains unchanged at every step. We show that the number of holes is at least O(n3∕4)after n steps.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135704384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that the uniform norm of generalized grey Brownian motion over the unit interval has an analytic density, excluding the special case of fractional Brownian motion. Our main result is an asymptotic expansion for the small ball probability of generalized grey Brownian motion, which extends to other norms on path space. The decay rate is not exponential but polynomial, of degree two. For the uniform norm and the Hölder norm, we also prove a large deviations estimate.
{"title":"Small ball probabilities and large deviations for grey Brownian motion","authors":"Stefan Gerhold","doi":"10.1214/23-ecp555","DOIUrl":"https://doi.org/10.1214/23-ecp555","url":null,"abstract":"We show that the uniform norm of generalized grey Brownian motion over the unit interval has an analytic density, excluding the special case of fractional Brownian motion. Our main result is an asymptotic expansion for the small ball probability of generalized grey Brownian motion, which extends to other norms on path space. The decay rate is not exponential but polynomial, of degree two. For the uniform norm and the Hölder norm, we also prove a large deviations estimate.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135704906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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