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Alea-Latin American Journal of Probability and Mathematical Statistics最新文献

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The GHS and other correlation inequalities for the two-star model 双星模型的GHS和其他相关不等式
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-07-19 DOI: 10.30757/ALEA.v19-64
A. Bianchi, Francesca Collet, Elena Magnanini
{"title":"The GHS and other correlation inequalities for the two-star model","authors":"A. Bianchi, Francesca Collet, Elena Magnanini","doi":"10.30757/ALEA.v19-64","DOIUrl":"https://doi.org/10.30757/ALEA.v19-64","url":null,"abstract":". We consider the two-star model, a family of exponential random graphs indexed by two real parameters, h and α , that rule respectively the total number of edges and the mutual dependence between them. Borrowing tools from statistical mechanics, we study different classes of correlation inequalities for edges, that naturally emerge while taking the partial derivatives of the (finite size) free energy. In particular, if α, h ≥ 0 , we derive first and second order correlation inequalities and then prove the so-called GHS inequality. As a consequence, under the above conditions on the parameters, the average edge density turns out to be an increasing and concave function of the parameter h , at any fixed size of the graph. Some of our results can be extended to more general classes of exponential random graphs.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47560457","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
Large Deviations for the SSEP with slow boundary: the non-critical case 具有慢边界的SSEP的大偏差：非关键情况
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-07-14 DOI: 10.30757/alea.v20-13
T. Franco, P. Gonccalves, A. Neumann
{"title":"Large Deviations for the SSEP with slow boundary: the non-critical case","authors":"T. Franco, P. Gonccalves, A. Neumann","doi":"10.30757/alea.v20-13","DOIUrl":"https://doi.org/10.30757/alea.v20-13","url":null,"abstract":"We prove a large deviations principle for the empirical measure of the one dimensional symmetric simple exclusion process in contact with reservoirs. The dynamics of the reservoirs is slowed down with respect to the dynamics of the system, that is, the rate at which the system exchanges particles with the boundary reservoirs is of order $n^{-theta}$, where $n$ is number of sites in the system, $theta$ is a non negative parameter, and the system is taken in the diffusive time scaling. Two regimes are studied here, the subcritical $thetain(0,1)$ whose hydrodynamic equation is the heat equation with Dirichlet boundary conditions and the supercritical $thetain(1,+infty)$ whose hydrodynamic equation is the heat equation with Neumann boundary conditions. In the subcritical case $thetain(0,1)$, the rate function that we obtain matches the rate function corresponding to the case $theta=0$ which was derived on previous works (see cite{blm,flm}), but the challenges we faced here are much trickier. In the supercritical case $thetain(1,+infty)$, the rate function is equal to infinity outside the set of trajectories which preserve the total mass, meaning that, despite the discrete system exchanges particles with the reservoirs, this phenomena has super-exponentially small probability in the diffusive scaling limit.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45737754","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
Convex minorants and the fluctuation theory of Lévy processes 凸极小子与Lévy过程的涨落理论
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-05-31 DOI: 10.30757/ALEA.v19-39
Jorge Ignacio Gonz'alez C'azares, Aleksandar Mijatovi'c
{"title":"Convex minorants and the fluctuation theory of Lévy processes","authors":"Jorge Ignacio Gonz'alez C'azares, Aleksandar Mijatovi'c","doi":"10.30757/ALEA.v19-39","DOIUrl":"https://doi.org/10.30757/ALEA.v19-39","url":null,"abstract":"We establish a novel characterisation of the law of the convex minorant of any L'evy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of L'evy processes. Our main result provides a new simple and self-contained approach to the fluctuation theory of L'evy processes, circumventing local time and excursion theory. Easy corollaries include classical theorems, such as Rogozin's regularity criterion, Spitzer's identities and the Wiener-Hopf factorisation, as well as a novel factorisation identity.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46595340","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: 9
The expected degree distribution in transient duplication divergence models 瞬态重复发散模型中的期望度分布
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-05-29 DOI: 10.30757/alea.v19-04
A. Barbour, Tiffany Y. Y. Lo
{"title":"The expected degree distribution in transient duplication divergence models","authors":"A. Barbour, Tiffany Y. Y. Lo","doi":"10.30757/alea.v19-04","DOIUrl":"https://doi.org/10.30757/alea.v19-04","url":null,"abstract":"We study the degree distribution of a randomly chosen vertex in a duplication–divergence graph, under a variety of different generalizations of the basic model of Bhan et al. (2002) and Vázquez et al. (2003). We pay particular attention to what happens when a non-trivial proportion of the vertices have large degrees, establishing a central limit theorem for the logarithm of the degree distribution. Our approach, as in Jordan (2018) and Hermann and Pfaffelhuber (2021), relies heavily on the analysis of related birth–catastrophe processes, and couplings are used to show that a number of different formulations of the process have asymptotically similar expected degree distributions.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45238899","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
Exponentially slow mixing and hitting times of rare events for a reaction–diffusion model 反应扩散模型中罕见事件的指数慢混合和撞击次数
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-05-27 DOI: 10.30757/alea.v19-48
K. Tsunoda
{"title":"Exponentially slow mixing and hitting times of rare events for a reaction–diffusion model","authors":"K. Tsunoda","doi":"10.30757/alea.v19-48","DOIUrl":"https://doi.org/10.30757/alea.v19-48","url":null,"abstract":". We consider the superposition of symmetric simple exclusion dynamics speeded-up in time, with spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We show that the mixing time has an exponential lower bound in the system size if the potential of the hydrodynamic equation has two or more local minima. We also apply our estimates to show that the normalized hitting times of rare events converge to a mean one exponential random variable if the potential has a unique minimum. deviation the quasi-potential and solutions to the","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69591340","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
Moderate deviation principles for bifurcating Markov chains: case of functions dependent of one variable 分叉马尔可夫链的中偏差原理：函数依赖于一个变量的情况
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-05-20 DOI: 10.30757/alea.v19-24
S. Valère, Bitseki Penda, Gorgui Gackou
{"title":"Moderate deviation principles for bifurcating Markov chains: case of functions dependent of one variable","authors":"S. Valère, Bitseki Penda, Gorgui Gackou","doi":"10.30757/alea.v19-24","DOIUrl":"https://doi.org/10.30757/alea.v19-24","url":null,"abstract":"The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be seen as the models which represent the evolution of a trait along a population where each individual has two offsprings. Unlike the previous results of Bitseki, Djellout &Guillin (2014), we consider here the case of functions which depend only on one variable. So, mainly inspired by the recent works of Bitseki &Delmas (2020) about the central limit theorem for general additive functionals of bifurcating Markov chains, we give here a moderate deviation principle for additive functionals of bifurcating Markov chains when the functions depend on one variable. This work is done under the uniform geometric ergodicity and the uniform ergodic property based on the second spectral gap assumptions. The proofs of our results are based on martingale decomposition recently developed by Bitseki &Delmas (2020) and on results of Dembo (1996), Djellout (2001) and Puhalski (1997).","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49042150","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
A stochastic adaptive dynamics model for bacterial populations with mutation, dormancy and transfer 具有突变、休眠和转移的细菌群体的随机自适应动力学模型
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-05-19 DOI: 10.30757/alea.v20-12
J. Blath, T. Paul, Andr'as T'obi'as
{"title":"A stochastic adaptive dynamics model for bacterial populations with mutation, dormancy and transfer","authors":"J. Blath, T. Paul, Andr'as T'obi'as","doi":"10.30757/alea.v20-12","DOIUrl":"https://doi.org/10.30757/alea.v20-12","url":null,"abstract":"This paper introduces a stochastic adaptive dynamics model for the interplay of several crucial traits and mechanisms in bacterial evolution, namely dormancy, horizontal gene transfer (HGT), mutation and competition. In particular, it combines the recent model of Champagnat, M'el'eard and Tran (2021) involving HGT with the model for competition-induced dormancy of Blath and T'obi'as (2020). Our main result is a convergence theorem which describes the evolution of the different traits in the population on a `doubly logarithmic scale' as piece-wise affine functions. Interestingly, even for a relatively small trait space, the limiting process exhibits a non-monotone dependence of the success of the dormancy trait on the dormancy initiation probability. Further, the model establishes a new `approximate coexistence regime' for multiple traits that has not been observed in previous literature.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47307384","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: 5
Stability of weak disorder phase for directed polymer with applications to limit theorems 定向聚合物弱无序相的稳定性及其极限定理的应用
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-05-10 DOI: 10.30757/ALEA.v20-31
S. Junk
{"title":"Stability of weak disorder phase for directed polymer with applications to limit theorems","authors":"S. Junk","doi":"10.30757/ALEA.v20-31","DOIUrl":"https://doi.org/10.30757/ALEA.v20-31","url":null,"abstract":"We study the directed polymer model in a bounded environment with bond disorder and show that, in the interior of the weak disorder phase, weak disorder continues to hold upon perturbation by a small bias. Using this stability result, we give a new proof for the central limit theorem (CLT) in probability for the directed polymer model in the interior of the weak disorder phase. We also show that the large deviation rate function agrees with that of the underlying random walk. For the Brownian polymer model, we improve the convergence in the CLT to almost sure convergence in the whole weak disorder phase. The main technical tools are a new moment bound from cite{J21_1} and a quantitative comparison between the associated martingales at different inverse temperatures.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48244668","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
Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case 随机Ising转移矩阵乘积的Lyapunov指数：平衡无序情形
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-04-30 DOI: 10.30757/ALEA.v19-27
G. Giacomin, R. L. Greenblatt
{"title":"Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case","authors":"G. Giacomin, R. L. Greenblatt","doi":"10.30757/ALEA.v19-27","DOIUrl":"https://doi.org/10.30757/ALEA.v19-27","url":null,"abstract":"We analyze the top Lyapunov exponent of the product of sequences of two by two matrices that appears in the analysis of several statistical mechanics models with disorder: for example these matrices are the transfer matrices for the nearest neighbor Ising chain with random external field, and the free energy density of this Ising chain is the Lyapunov exponent we consider. We obtain the sharp behavior of this exponent in the large interaction limit when the external field is centered: this balanced case turns out to be critical in many respects. From a mathematical standpoint we precisely identify the behavior of the top Lyapunov exponent of a product of two dimensional random matrices close to a diagonal random matrix for which top and bottom Lyapunov exponents coincide. In particular, the Lyapunov exponent is only $log$-H\"older continuous.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47582416","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 β-Delaunay tessellation III: Kendall’s problem and limit theorems in high dimensions β-Delaunay镶嵌Ⅲ：高维上的Kendall问题和极限定理
IF 0.7 4区 数学
Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-04-15 DOI: 10.30757/ALEA.v19-02
A. Gusakova, Z. Kabluchko, Christoph Thale
{"title":"The β-Delaunay tessellation III: Kendall’s problem and limit theorems in high dimensions","authors":"A. Gusakova, Z. Kabluchko, Christoph Thale","doi":"10.30757/ALEA.v19-02","DOIUrl":"https://doi.org/10.30757/ALEA.v19-02","url":null,"abstract":"The $beta$-Delaunay tessellation in $mathbb{R}^{d-1}$ is a generalization of the classical Poisson-Delaunay tessellation. As a first result of this paper we show that the shape of a weighted typical cell of a $beta$-Delaunay tessellation, conditioned on having large volume, is close to the shape of a regular simplex in $mathbb{R}^{d-1}$. This generalizes earlier results of Hug and Schneider about the typical (non-weighted) Poisson-Delaunay simplex. Second, the asymptotic behaviour of the volume of weighted typical cells in high-dimensional $beta$-Delaunay tessellation is analysed, as $dtoinfty$. In particular, various high dimensional limit theorems, such as quantitative central limit theorems as well as moderate and large deviation principles, are derived.","PeriodicalId":49244,"journal":{"name":"Alea-Latin American Journal of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49369872","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
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