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Time reversal of spinal processes for linear and non-linear branching processes near stationarity 接近平稳的线性和非线性分支过程脊柱过程的时间反转
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-13 DOI: 10.1214/23-ejp911
Benoît Henry, S. M'el'eard, V. Tran
{"title":"Time reversal of spinal processes for linear and non-linear branching processes near stationarity","authors":"Benoît Henry, S. M'el'eard, V. Tran","doi":"10.1214/23-ejp911","DOIUrl":"https://doi.org/10.1214/23-ejp911","url":null,"abstract":"We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be approximated in large population by a non-linear PDE with a non-local mutation operator. Using the fact that this PDE admits a non-trivial stationary solution, we can approximate the non-linear stochastic population process by a linear birth-death process where the interactions are frozen, as long as the population remains close to this equilibrium. This allows us to derive, when the population is large, the equation satisfied by the ancestral lineage of an individual uniformly sampled at a fixed time $T$, which is the path constituted of the traits of the ancestors of this individual in past times $tleq T$. This process is a time inhomogeneous Markov process, but we show that the time reversal of this process possesses a very simple structure (e.g. time-homogeneous and independent of $T$). This extends recent results where the authors studied a similar model with a Laplacian operator but where the methods essentially relied on the Gaussian nature of the mutations.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41947489","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
Large deviations for Ablowitz-Ladik lattice, and the Schur flow Ablowitz-Ladik晶格和Schur流的大偏差
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-10 DOI: 10.1214/23-EJP941
Guido Mazzuca, Ronan Memin
{"title":"Large deviations for Ablowitz-Ladik lattice, and the Schur flow","authors":"Guido Mazzuca, Ronan Memin","doi":"10.1214/23-EJP941","DOIUrl":"https://doi.org/10.1214/23-EJP941","url":null,"abstract":"We consider the Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, and the Schur flow. We derive large deviations principles for the distribution of the empirical measures of the equilibrium measures for these ensembles. As a consequence, we deduce their almost sure convergence. Moreover, we are able to characterize their limit in terms of the equilibrium measure of the Circular, and the Jacobi beta ensemble respectively.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42646790","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: 4
On joint properties of vertices with a given degree or label in the random recursive tree 随机递归树中具有给定度或标签的顶点的联合性质
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp877
B. Lodewijks
{"title":"On joint properties of vertices with a given degree or label in the random recursive tree","authors":"B. Lodewijks","doi":"10.1214/22-ejp877","DOIUrl":"https://doi.org/10.1214/22-ejp877","url":null,"abstract":"In this paper, we study the joint behaviour of the degree, depth and label of and graph distance between high-degree vertices in the random recursive tree. We generalise the results obtained by Eslava and extend these to include the labels of and graph distance between high-degree vertices. The analysis of both these two properties of high-degree vertices is novel, in particular in relation to the behaviour of the depth of such vertices. In passing, we also obtain results for the joint behaviour of the degree and depth of and graph distance between any fixed number of vertices with a prescribed label. This combines several isolated results on the degree and depth of and graph distance between vertices with a prescribed label already present in the literature. Furthermore, we extend these results to hold jointly for any number of fixed vertices and improve these results by providing more detailed descriptions of the distributional limits. Our analysis is based on a correspondence between the random recursive tree and a representation of the Kingman $n$-coalescent.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43560161","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
Large sample correlation matrices: a comparison theorem and its applications 大样本相关矩阵:一个比较定理及其应用
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp817
J. Heiny
{"title":"Large sample correlation matrices: a comparison theorem and its applications","authors":"J. Heiny","doi":"10.1214/22-ejp817","DOIUrl":"https://doi.org/10.1214/22-ejp817","url":null,"abstract":"In this paper, we show that the diagonal of a high-dimensional sample covariance matrix stemming from $n$ independent observations of a $p$-dimensional time series with finite fourth moments can be approximated in spectral norm by the diagonal of the population covariance matrix. We assume that $n,pto infty$ with $p/n$ tending to a constant which might be positive or zero. As applications, we provide an approximation of the sample correlation matrix ${mathbf R}$ and derive a variety of results for its eigenvalues. We identify the limiting spectral distribution of ${mathbf R}$ and construct an estimator for the population correlation matrix and its eigenvalues. Finally, the almost sure limits of the extreme eigenvalues of ${mathbf R}$ in a generalized spiked correlation model are analyzed.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44124562","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
Entanglement percolation and spheres in Zd Zd中的纠缠渗流和球体
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp816
O. Couronne
{"title":"Entanglement percolation and spheres in Zd","authors":"O. Couronne","doi":"10.1214/22-ejp816","DOIUrl":"https://doi.org/10.1214/22-ejp816","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49614268","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
Shaken dynamics on the 3d cubic lattice 三维立方晶格上的振动动力学
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp803
B. Scoppola, A. Troiani, Matteo Veglianti
{"title":"Shaken dynamics on the 3d cubic lattice","authors":"B. Scoppola, A. Troiani, Matteo Veglianti","doi":"10.1214/22-ejp803","DOIUrl":"https://doi.org/10.1214/22-ejp803","url":null,"abstract":"On the space of $pm 1$ spin configurations on the 3$d$-square lattice, we consider the emph{shaken dynamics}, a parallel Markovian dynamics that can be interpreted in terms of Probabilistic Cellular Automata. The transition probabilities are defined in terms of pair ferromagnetic Ising-type Hamiltonians with nearest neighbor interaction $J$, depending on an additional parameter $q$, measuring the tendency of the system to remain locally in the same state. Odd times and even times have different transition probabilities. We compute the stationary measure of the shaken dynamics and we investigate its relation with the Gibbs measure for the 3$d$ Ising model. It turns out that the two parameters $J$ and $q$ tune the geometry of the underlying lattice. We conjecture the existence of unique line of critical points in $J-q$ plane. By a judicious use of perturbative methods we delimit the region where such curve must lie and we perform numerical simulation to determine it. Our method allows us to find in a unified way the critical values of $J$ for Ising model with first neighbors interaction, defined on a whole class of lattices, intermediate between the two-dimensional hexagonal and the three-dimensional cubic one, such as, for example, the tetrahedral lattice. Finally we estimate the critical exponents of the magnetic susceptibility and show that our model captures a dimensional transition in the geometry of the system at $q = 0$.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46057265","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
Variable speed symmetric random walk driven by the simple symmetric exclusion process 简单对称排斥过程驱动的变速对称随机游动
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/21-ejp735
O. Menezes, Jonathon Peterson, Yong-Xiao Xie
{"title":"Variable speed symmetric random walk driven by the simple symmetric exclusion process","authors":"O. Menezes, Jonathon Peterson, Yong-Xiao Xie","doi":"10.1214/21-ejp735","DOIUrl":"https://doi.org/10.1214/21-ejp735","url":null,"abstract":"We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of the random walk in a balanced random environment, for which the weak quenched limit is constructed as a function of the invariant measure of the environment viewed from the walk. We bypass the need to show the existence of this invariant measure. Instead, we find the limit of the quadratic variation of the walk and give an explicit formula for it.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49627692","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
The overlap distribution at two temperatures for the branching Brownian motion 分支布朗运动在两个温度下的重叠分布
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp841
Benjamin Bonnefont
{"title":"The overlap distribution at two temperatures for the branching Brownian motion","authors":"Benjamin Bonnefont","doi":"10.1214/22-ejp841","DOIUrl":"https://doi.org/10.1214/22-ejp841","url":null,"abstract":"We study the overlap distribution of two particles chosen under the Gibbs measure at two temperatures for the branching Brownian motion. We first prove the convergence of the overlap distribution using the extended convergence of the extremal process obtained by Bovier and Hartung [8]. We then prove that the mean overlap of two points chosen at different temperatures is strictly smaller than in Derrida’s random energy model. The proof of this last result is achieved with the description of the decoration point process obtained by Aïdékon, Berestycki, Brunet and Shi [1]. To our knowledge, it is the first time that this description is being used. Keywords— Branching Brownian motion, Gibbs measure, overlap distribution, random energy model.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46487087","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
On non-extinction in a Fleming-Viot-type particle model with Bessel drift 关于带有贝塞尔漂移的Fleming-Viot型粒子模型中的非消光
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp866
Martin Kolb, Matthias Liesenfeld
{"title":"On non-extinction in a Fleming-Viot-type particle model with Bessel drift","authors":"Martin Kolb, Matthias Liesenfeld","doi":"10.1214/22-ejp866","DOIUrl":"https://doi.org/10.1214/22-ejp866","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42410600","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
Norms of randomized circulant matrices 随机循环矩阵的范数
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2022-01-01 DOI: 10.1214/22-ejp799
R. Lata, W. Świątkowski
{"title":"Norms of randomized circulant matrices","authors":"R. Lata, W. Świątkowski","doi":"10.1214/22-ejp799","DOIUrl":"https://doi.org/10.1214/22-ejp799","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45653526","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
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