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Electronic Communications in Probability最新文献

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Sharp phase transition for Cox percolation Cox渗流的急剧相变
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp487
C. Hirsch, B. Jahnel, S. Muirhead
{"title":"Sharp phase transition for Cox percolation","authors":"C. Hirsch, B. Jahnel, S. Muirhead","doi":"10.1214/22-ecp487","DOIUrl":"https://doi.org/10.1214/22-ecp487","url":null,"abstract":"We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence, satisfies a local boundedness condition and can be constructed from a discrete iid random field, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction that allows us to compare different notions of influence.","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":"47500768","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
Erratum: The remainder in the renewal theorem 勘误表：更新定理中的余数
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp456
R. Doney
{"title":"Erratum: The remainder in the renewal theorem","authors":"R. Doney","doi":"10.1214/22-ecp456","DOIUrl":"https://doi.org/10.1214/22-ecp456","url":null,"abstract":"We point out an error in \"The remainder in the renewal theorem\", and show that the result is essentially correct in two important special cases.","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":"49507916","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
The logarithmic anti-derivative of the Baik-Rains distribution satisfies the KP equation Baik-Rains分布的对数反导数满足KP方程
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp469
Xincheng Zhang
{"title":"The logarithmic anti-derivative of the Baik-Rains distribution satisfies the KP equation","authors":"Xincheng Zhang","doi":"10.1214/22-ecp469","DOIUrl":"https://doi.org/10.1214/22-ecp469","url":null,"abstract":"It has been discovered that the Kadomtsev-Petviashvili (KP) equation governs the distribution of the fluctuation of many random growth models. In particular, the Tracy-Widom distributions appear as special self-similar solutions of the KP equation. We prove that the anti-derivative of the Baik-Rains distribution, which governs the fluctuation of the models in the KPZ universality class starting with stationary initial data, satisfies the KP equation. The result is first derived formally by taking a limit of the generating function of the KPZ equation, which satisfies the KP equation. Then we prove it directly using the explicit Painlevé II formulation of the Baik-Rains distribution. the long-time fluctuations of models which belong to the KPZ universality class. A 1 ( x ) is a stationary process, whose one-point distribution is the Tracy-Widom GOE distribution. The one point marginal of A 2 ( x ) is given by the Tracy-Widom GUE distribution. The one point marginal of A stat ( x ) is given by the Baik-Rains distribution.","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":"49510101","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
Quasi-sure non-self-intersection for rough differential equations driven by fractional Brownian motion 分数阶布朗运动驱动粗糙微分方程的准确定非自交
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp454
O. Cheng, William Roberson-Vickery
{"title":"Quasi-sure non-self-intersection for rough differential equations driven by fractional Brownian motion","authors":"O. Cheng, William Roberson-Vickery","doi":"10.1214/22-ecp454","DOIUrl":"https://doi.org/10.1214/22-ecp454","url":null,"abstract":"In this paper we study the self-intersection of paths solving elliptic stochastic differential equations driven by fractional Brownian motion. We show that such a path has no self-intersection – except for paths forming a set of zero (r, q)-capacity in the sample space – provided the dimension d of the space and the Hurst parameter H satisfy the inequality d > rq + 2/H. This inequality is sharp in the case of brownian motion and fractional brownian motion according to existing results. Various results exist for the critical case where d = rq + 4 for Brownian motion.","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":"43809384","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
The weak functional representation of historical martingales 历史鞅的弱函数表示
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp492
C. Mandler, L. Overbeck
{"title":"The weak functional representation of historical martingales","authors":"C. Mandler, L. Overbeck","doi":"10.1214/22-ecp492","DOIUrl":"https://doi.org/10.1214/22-ecp492","url":null,"abstract":"A weak extension of the Dupire derivative is derived, which turns out to be the adjoint operator of the integral with respect to the martingale measure associated with the historical Brownian motion a benchmark example of a measure valued process. This extension yields the explicit form of the martingale representation of historical functionals, which we compare to a classical result on the representation of historical functionals derived in [7].","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":"44525313","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
A note on recovering the Brownian motion component from a Lévy process 关于从Lévy过程中恢复布朗运动分量的一个注记
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ecp477
K. Borovkov
{"title":"A note on recovering the Brownian motion component from a Lévy process","authors":"K. Borovkov","doi":"10.1214/22-ecp477","DOIUrl":"https://doi.org/10.1214/22-ecp477","url":null,"abstract":"González Cázares and Ivanovs (2021) suggested a new method for “recovering” the Brownian motion component from the trajectory of a Lévy process that required sampling from an independent Brownian motion process. We show that such a procedure works equally well without any additional source of randomness if one uses normal quantiles instead of the ordered increments of the auxiliary Brownian motion 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":"46442075","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
Chase-escape on the configuration model 配置模型上的追逐逃逸
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-12-14 DOI: 10.1214/22-ecp470
E. Bernstein, Clare Hamblen, M. Junge, Lily Reeves
{"title":"Chase-escape on the configuration model","authors":"E. Bernstein, Clare Hamblen, M. Junge, Lily Reeves","doi":"10.1214/22-ecp470","DOIUrl":"https://doi.org/10.1214/22-ecp470","url":null,"abstract":"Chase-escape is a competitive growth process in which red particles spread to adjacent empty sites according to a rate-$lambda$ Poisson process while being chased and consumed by blue particles according to a rate-$1$ Poisson process. Given a growing sequence of finite graphs, the critical rate $lambda_c$ is the largest value of $lambda$ for which red fails to reach a positive fraction of the vertices with high probability. We provide a conjecturally sharp lower bound and an implicit upper bound on $lambda_c$ for supercritical random graphs sampled from the configuration model with independent and identically distributed degrees with finite second moment. We additionally show that the expected number of sites occupied by red undergoes a phase transition and identify the location of this transition.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42606919","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
Stochastic approximation of the paths of killed Markov processes conditioned on survival 以生存为条件的死亡马尔可夫过程路径的随机逼近
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-12-06 DOI: 10.1214/22-ecp475
Oliver Tough
{"title":"Stochastic approximation of the paths of killed Markov processes conditioned on survival","authors":"Oliver Tough","doi":"10.1214/22-ecp475","DOIUrl":"https://doi.org/10.1214/22-ecp475","url":null,"abstract":"Reinforced processes are known to provide a stochastic representation for the quasi-stationary distribution of a given killed Markov process – describing the killed Markov process at fixed time instants. In this paper we shall adapt the construction to provide a pathwise description. We also obtain a stochastic approximation for the quasi-limiting distributions of reducible killed Markov processes as a corollary.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41932513","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
Dominating occupancy processes by the independent site approximation 通过独立场地近似支配占用过程
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-12-06 DOI: 10.1214/22-ecp499
R. McVinish
{"title":"Dominating occupancy processes by the independent site approximation","authors":"R. McVinish","doi":"10.1214/22-ecp499","DOIUrl":"https://doi.org/10.1214/22-ecp499","url":null,"abstract":"Occupancy processes are a broad class of discrete time Markov chains on ${0,1}^{n}$ encompassing models from diverse areas. This model is compared to a collection of $n$ independent Markov chains on ${0,1}$, which we call the independent site model. We establish conditions under which an occupancy process is smaller in the lower orthant order than the independent site model. An analogous result for spin systems follows by a limiting argument.}","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46252478","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
Marginals of a spherical spin glass model with correlated disorder 具有相关无序的球形自旋玻璃模型的边缘
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2021-12-03 DOI: 10.1214/22-ecp489
Jean Barbier, M. S'aenz
{"title":"Marginals of a spherical spin glass model with correlated disorder","authors":"Jean Barbier, M. S'aenz","doi":"10.1214/22-ecp489","DOIUrl":"https://doi.org/10.1214/22-ecp489","url":null,"abstract":"In this paper we prove the weak convergence, in a high-temperature phase, of the finite marginals of the Gibbs measure associated to a symmetric spherical spin glass model with correlated couplings towards an explicit asymptotic decoupled measure. We also provide upper bounds for the rate of convergence in terms of the one of the energy per variable. Furthermore, we establish a concentration inequality for bounded functions under a higher temperature condition. These results are exemplified by analysing the asymptotic behaviour of the empirical mean of coordinate-wise functions of samples from the Gibbs measure of the model.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45623919","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
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