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Electronic Communications in Probability最新文献

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A matrix-valued Schoenberg’s problem and its applications 矩阵值勋伯格问题及其应用
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp562
Pavel Ievlev, Svyatoslav Novikov
{"title":"A matrix-valued Schoenberg’s problem and its applications","authors":"Pavel Ievlev, Svyatoslav Novikov","doi":"10.1214/23-ecp562","DOIUrl":"https://doi.org/10.1214/23-ecp562","url":null,"abstract":"In this paper we present a criterion for positive definiteness of the matrix-valued function f(t):=exp(−|t|α[B++B−sign(t)]), where α∈(0,2] and B± are real symmetric and antisymmetric d×d matrices. We also find a criterion for positive definiteness of its multidimensional generalization f(t):=exp(−∫Sd−1|t⊤s|α[B++B−sign(t⊤s)]dΛ(s)) where Λ is a finite measure on the unit sphere Sd−1⊂Rd under a more restrictive assumption that B± commute and are normal. The associated stationary Gaussian random field may be viewed as as a generalization of the univariate fractional Ornstein-Uhlenbeck process. This generalization turns out to be particularly useful for the asymptotic analysis of Rd-valued Gaussian random fields. Another possible application of these findings may concern variogram modelling and general stationary time series analysis.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":"44 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":"135704903","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
Sensitive bootstrap percolation second term 敏感自举渗流第二项
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp535
Ivailo Hartarsky
{"title":"Sensitive bootstrap percolation second term","authors":"Ivailo Hartarsky","doi":"10.1214/23-ecp535","DOIUrl":"https://doi.org/10.1214/23-ecp535","url":null,"abstract":"In modified two-neighbour bootstrap percolation in two dimensions each site of $mathbb Z^2$ is initially independently infected with probability $p$ and on each discrete time step one additionally infects sites with at least two non-opposite infected neighbours. In this note we establish that for this model the second term in the asymptotics of the infection time $tau$ unexpectedly scales differently from the classical two-neighbour model, in which arbitrary two infected neighbours are required. More precisely, we show that for modified bootstrap percolation with high probability as $pto0$ it holds that [taule expleft(frac{pi^2}{6p}-frac{clog(1/p)}{sqrt p}right)] for some positive constant $c$, while the classical model is known to lack the logarithmic factor.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48395239","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
Large deviations for the greedy exploration process on configuration models 贪心勘探过程在组态模型上的大偏差
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp541
Bermolen Paola, Goicoechea Valeria, Jonckheere Matthieu
{"title":"Large deviations for the greedy exploration process on configuration models","authors":"Bermolen Paola, Goicoechea Valeria, Jonckheere Matthieu","doi":"10.1214/23-ecp541","DOIUrl":"https://doi.org/10.1214/23-ecp541","url":null,"abstract":"We prove a large deviation principle for the greedy exploration of configuration models, building on a time-discretized version of the method proposed by [2] and [4] for jointly constructing a random graph from a given degree sequence and its exploration. The proof of this result follows the general strategy to study large deviations of processes proposed by [9], based on the convergence of non-linear semigroups. We provide an intuitive interpretation of the LD cost function using Crámer’s theorem for the average of random variables with appropriate distribution, depending on the degree distribution of explored nodes. The rate function can be expressed in a closed-form formula, and the large deviations trajectories can be obtained through explicit associated optimization problems. We then deduce large deviations results for the size of the independent set constructed by the algorithm. As a particular case, we analyze these results for d-regular graphs.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":"1 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":"136003485","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
The existence of the least favorable noise 最不利噪声的存在
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp533
Dongzhou Huang
{"title":"The existence of the least favorable noise","authors":"Dongzhou Huang","doi":"10.1214/23-ecp533","DOIUrl":"https://doi.org/10.1214/23-ecp533","url":null,"abstract":"Suppose that a random variable $X$ of interest is observed. This paper concerns\"the least favorable noise\"$hat{Y}_{epsilon}$, which maximizes the prediction error $E [X - E[X|X+Y]]^2 $ (or minimizes the variance of $E[X| X+Y]$) in the class of $Y$ with $Y$ independent of $X$ and $mathrm{var} Y leq epsilon^2$. This problem was first studied by Ernst, Kagan, and Rogers ([3]). In the present manuscript, we show that the least favorable noise $hat{Y}_{epsilon}$ must exist and that its variance must be $epsilon^2$. The proof of existence relies on a convergence result we develop for variances of conditional expectations. Further, we show that the function $inf_{mathrm{var} Y leq epsilon^2} , mathrm{var} , E[X|X+Y]$ is both strictly decreasing and right continuous in $epsilon$.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47464978","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
Corrigendum to: The contact process on periodic trees 勘误表：周期树上的接触过程
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp518
Xiangying Huang, R. Durrett
{"title":"Corrigendum to: The contact process on periodic trees","authors":"Xiangying Huang, R. Durrett","doi":"10.1214/23-ecp518","DOIUrl":"https://doi.org/10.1214/23-ecp518","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44393029","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
Brownian snails with removal die out in one dimension 带移除的布朗蜗牛在一维中死亡
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp551
Ivailo Hartarsky, Lyuben Lichev
{"title":"Brownian snails with removal die out in one dimension","authors":"Ivailo Hartarsky, Lyuben Lichev","doi":"10.1214/23-ecp551","DOIUrl":"https://doi.org/10.1214/23-ecp551","url":null,"abstract":"Brownian snails with removal is a spatial epidemic model defined as follows. Initially, a homogeneous Poisson process of susceptible particles on Rd with intensity λ>0 is deposited and a single infected one is added at the origin. Each particle performs an independent standard Brownian motion. Each susceptible particle is infected immediately when it is within distance 1 from an infected particle. Each infected particle is removed at rate α>0, and removed particles remain such forever. Answering a question of Grimmett and Li, we prove that in one dimension, for all values of λ and α, the infection almost surely dies out.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":"24 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":"135450721","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
The scaling limit of the weakly self-avoiding walk on a high-dimensional torus 高维环面上弱自避行走的尺度极限
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp531
Emmanuel Michta
{"title":"The scaling limit of the weakly self-avoiding walk on a high-dimensional torus","authors":"Emmanuel Michta","doi":"10.1214/23-ecp531","DOIUrl":"https://doi.org/10.1214/23-ecp531","url":null,"abstract":"We prove that the scaling limit of the weakly self-avoiding walk on a d-dimensional discrete torus is Brownian motion on the continuum torus if the length of the rescaled walk is o(V1∕2) where V is the volume (number of points) of the torus and if d>4. We also prove that the diffusion constant of the resulting torus Brownian motion is the same as the diffusion constant of the scaling limit of the usual weakly self-avoiding walk on Zd. This provides further manifestation of the fact that the weakly self-avoiding walk model on the torus does not feel that it is on the torus up until it reaches about V1∕2 steps, which we believe is sharp.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":"18 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":"135733740","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
Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments 一类无界环境中定向聚合物弱无序相的矩表征
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp545
Ryoki Fukushima, Stefan Junk
{"title":"Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments","authors":"Ryoki Fukushima, Stefan Junk","doi":"10.1214/23-ecp545","DOIUrl":"https://doi.org/10.1214/23-ecp545","url":null,"abstract":"For a directed polymer model in random environment, a characterization of the weak disorder phase in terms of the moment of the renormalized partition function has been proved in [S. Junk: Communications in Mathematical Physics 389, 1087–1097 (2022)]. We extend this characterization to a large class of unbounded environments which includes many commonly used distributions.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":"17 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":"135958441","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
On smooth approximations in the Wasserstein space 关于Wasserstein空间中的光滑逼近
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ECP538
Andrea Cosso, Mattia Martini
{"title":"On smooth approximations in the Wasserstein space","authors":"Andrea Cosso, Mattia Martini","doi":"10.1214/23-ECP538","DOIUrl":"https://doi.org/10.1214/23-ECP538","url":null,"abstract":"In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are able to construct a sequence of infinitely differentiable functions having the same Lipschitz constant as the original function. This solves an open problem raised in [11]. For (resp. twice) continuously differentiable function, we show that our approximation also holds for the first-order derivative (resp. second-order derivatives), therefore solving another open problem raised in [11].","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45296634","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
Generating discrete uniform distribution from a biased coin using number-theoretic method 用数论方法生成有偏硬币的离散均匀分布
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp537
Xiaoyu Lei
{"title":"Generating discrete uniform distribution from a biased coin using number-theoretic method","authors":"Xiaoyu Lei","doi":"10.1214/23-ecp537","DOIUrl":"https://doi.org/10.1214/23-ecp537","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41951614","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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