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Electronic Communications in Probability最新文献

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Parabolic Anderson model with rough noise in space and rough initial conditions 空间中具有粗糙噪声和粗糙初始条件的抛物型Anderson模型
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp506
R. Balan, Le Chen, Yiping Ma
{"title":"Parabolic Anderson model with rough noise in space and rough initial conditions","authors":"R. Balan, Le Chen, Yiping Ma","doi":"10.1214/22-ecp506","DOIUrl":"https://doi.org/10.1214/22-ecp506","url":null,"abstract":"In this note, we consider the parabolic Anderson model on R + × R , driven by a Gaussian noise which is fractional in time with index H 0 > 1 / 2 and fractional in space with index 0 < H < 1 / 2 such that H 0 + H > 3 / 4. Under a general condition on the initial data, we prove the existence and uniqueness of the mild solution and obtain its exponential upper bounds in time for all p -th moments with p ≥ 2.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49497306","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}
引用次数: 1
Subcritical bootstrap percolation via Toom contours 通过Toom等值线的亚临界自举渗流
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp496
Ivailo Hartarsky, R. Szab'o
{"title":"Subcritical bootstrap percolation via Toom contours","authors":"Ivailo Hartarsky, R. Szab'o","doi":"10.1214/22-ecp496","DOIUrl":"https://doi.org/10.1214/22-ecp496","url":null,"abstract":"In this note we provide an alternative proof of the fact that subcritical bootstrap percolation models have a positive critical probability in any dimension. The proof relies on a recent extension [18] of the classical framework of Toom [20]. This approach is not only simpler than the original multi-scale renormalisation proof of the result in two and more dimensions [1, 2], but also gives significantly better bounds. As a byproduct, we improve the best known bounds for the stability threshold of Toom’s North-East-Center majority rule cellular automaton.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43100680","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}
引用次数: 3
Large-time and small-time behaviors of the spectral heat content for time-changed stable processes 时变稳定过程光谱热含量的大时间和小时间行为
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp478
Kei Kobayashi, Hyunchul Park
{"title":"Large-time and small-time behaviors of the spectral heat content for time-changed stable processes","authors":"Kei Kobayashi, Hyunchul Park","doi":"10.1214/22-ecp478","DOIUrl":"https://doi.org/10.1214/22-ecp478","url":null,"abstract":"We study the large-time and small-time asymptotic behaviors of the spectral heat content for time-changed stable processes, where the time change belongs to a large class of inverse subordinators. For the large-time behavior, the spectral heat content decays polynomially with the decay rate determined by the Laplace exponent of the underlying subordinator, which is in sharp contrast to the exponential decay observed in the case when the time change is a subordinator. On the other hand, the small-time behavior exhibits three different decay regimes, where the decay rate is determined by both the Laplace exponent and the index of the stable process.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47368804","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}
引用次数: 2
Zero bias enhanced Stein couplings 零偏置增强型Stein联轴器
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ECP504
L. Goldstein
{"title":"Zero bias enhanced Stein couplings","authors":"L. Goldstein","doi":"10.1214/22-ECP504","DOIUrl":"https://doi.org/10.1214/22-ECP504","url":null,"abstract":"The Stein couplings of Chen and Roellin (2010) vastly expanded the range of applications for which coupling constructions in Stein's method for normal approximation could be applied, and subsumed both Stein's classical exchangeable pair, as well as the size bias coupling. A further simple generalization includes zero bias couplings, and also allows for situations where the coupling is not exact. The zero bias versions result in bounds for which often tedious computations of a variance of a conditional expectation is not required. An example to the Lightbulb process shows that even though the method may be simple to apply, it may yield improvements over previous results that had achieved bounds with optimal rates and small, explicit constants.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44555929","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}
引用次数: 0
Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension 任意维连续PAM及其相关模型的随机电位转换正则化
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp490
F. Bechtold
{"title":"Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension","authors":"F. Bechtold","doi":"10.1214/22-ecp490","DOIUrl":"https://doi.org/10.1214/22-ecp490","url":null,"abstract":"We study a regularization by noise phenomenon for the continuous parabolic Anderson model with a potential shifted along paths of fractional Brownian motion. We demonstrate that provided the Hurst parameter is chosen sufficiently small, this shift allows to establish well-posedness and stability to the corresponding problem - without the need of renormalization - in any dimension. We moreover provide a robustified Feynman-Kac type formula for the unique solution to the regularized problem building upon regularity estimates for the local time of fractional Brownian motion as well as non-linear Young integration.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44368701","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}
引用次数: 2
The completely delocalized region of the Erdős-Rényi graph Erdős-Rényi图的完全离域区域
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp450
Johannes Alt, Raphael Ducatez, A. Knowles
{"title":"The completely delocalized region of the Erdős-Rényi graph","authors":"Johannes Alt, Raphael Ducatez, A. Knowles","doi":"10.1214/22-ecp450","DOIUrl":"https://doi.org/10.1214/22-ecp450","url":null,"abstract":"We analyse the eigenvectors of the adjacency matrix of the Erdős-Rényi graph on N vertices with edge probability d N . We determine the full region of delocalization by determining the critical values of d log N down to which delocalization persists: for d log N > 1 log 4−1 all eigenvectors are completely delocalized, and for d log N > 1 all eigenvectors with eigenvalues away from the spectral edges are completely delocalized. Below these critical values, it is known [1, 3] that localized eigenvectors exist in the corresponding spectral regions.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47542430","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}
引用次数: 4
The maximum domain of attraction of multivariate extreme value distributions is small 多元极值分布的最大吸引域很小
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp501
P. Leonetti, A. K. Chokami
{"title":"The maximum domain of attraction of multivariate extreme value distributions is small","authors":"P. Leonetti, A. K. Chokami","doi":"10.1214/22-ecp501","DOIUrl":"https://doi.org/10.1214/22-ecp501","url":null,"abstract":". Consider the set of Borel probability measures on R k and endow it with the topology of weak convergence. We show that the subset of all probability measures which belong to the domain of attraction of some multivariate extreme value distributions is dense and of the first Baire category. In addition, the analogue result holds in the context of free probability theory.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44224546","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}
引用次数: 2
Weak-type estimates for martingale maximal functions 鞅极大函数的弱型估计
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp494
A. Osȩkowski, Mateusz Wojtas
{"title":"Weak-type estimates for martingale maximal functions","authors":"A. Osȩkowski, Mateusz Wojtas","doi":"10.1214/22-ecp494","DOIUrl":"https://doi.org/10.1214/22-ecp494","url":null,"abstract":"The paper contains the study of sharp extensions of weak-type estimates for a martingale maximal function. Given 1 < p < ∞ and a pair ( x, y ) of nonnegative numbers satisfying x p ≤ y , we identify the optimal upper bounds for (cid:107)| sup n f n |(cid:107) p, ∞ , for nonnegative martingales f = ( f n ) n ≥ 0 satisfying (cid:107) f (cid:107) 1 = x and (cid:107) f (cid:107) pp = y .","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46138797","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}
引用次数: 0
On the central limit theorem for stationary random fields under L1-projective condition l1 -射影条件下平稳随机场的中心极限定理
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp486
H. Lin, F. Merlevède, D. Volný
{"title":"On the central limit theorem for stationary random fields under L1-projective condition","authors":"H. Lin, F. Merlevède, D. Volný","doi":"10.1214/22-ecp486","DOIUrl":"https://doi.org/10.1214/22-ecp486","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41419643","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}
引用次数: 0
Gaussian fluctuations of replica overlap in directed polymers 定向聚合物中复制重叠的高斯涨落
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp476
Yu Gu, T. Komorowski
{"title":"Gaussian fluctuations of replica overlap in directed polymers","authors":"Yu Gu, T. Komorowski","doi":"10.1214/22-ecp476","DOIUrl":"https://doi.org/10.1214/22-ecp476","url":null,"abstract":". In this short note, we prove a central limit theorem for a type of replica overlap of the Brownian directed polymer in a Gaussian random environment, in the low temperature regime and in all dimensions. The proof relies on a superconcentration result for the KPZ equation driven by a spatially mollified noise, which is inspired by the recent work of Chatterjee [14].","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48840622","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}
引用次数: 0
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