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Annales De L Institut Henri Poincare-probabilites Et Statistiques最新文献

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Evolution of the ABC model among the segregated configurations in the zero-temperature limit 零温度极限下分离构型中ABC模型的演化
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-03-19 DOI: 10.1214/14-AIHP648
R. Misturini
{"title":"Evolution of the ABC model among the segregated configurations in the zero-temperature limit","authors":"R. Misturini","doi":"10.1214/14-AIHP648","DOIUrl":"https://doi.org/10.1214/14-AIHP648","url":null,"abstract":"We consider the ABC model on a ring in a strongly asymmetric regime. The main result asserts that the particles almost always form three pure domains (one of each species) and that this segregated shape evolves, in a proper time scale, as a Brownian motion on the circle, which may have a drift. This is, to our knowledge, the first proof of a zero-temperature limit for a non-reversible dynamics whose invariant measure is not explicitly known.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"127 1","pages":"669-702"},"PeriodicalIF":1.5,"publicationDate":"2014-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74145082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 10
Universality of the ESD for a fixed matrix plus small random noise: A stability approach 固定矩阵加小随机噪声的静电放电的通用性:一种稳定性方法
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-03-18 DOI: 10.1214/15-AIHP702
Philip Matchett Wood
{"title":"Universality of the ESD for a fixed matrix plus small random noise: A stability approach","authors":"Philip Matchett Wood","doi":"10.1214/15-AIHP702","DOIUrl":"https://doi.org/10.1214/15-AIHP702","url":null,"abstract":"We study the empirical spectral distribution (ESD) in the limit where n goes to infinity of a fixed n by n matrix M_n plus small random noise of the form f(n)X_n, where X_n has iid mean 0, variance 1/n entries and f(n) goes to 0 as n goes to infinity. It is known for certain M_n, in the case where X_n is iid complex Gaussian, that the limiting distribution of the ESD of M_n+f(n)X_n can be dramatically different from that for M_n. We prove a general universality result showing, with some conditions on M_n and f(n), that the limiting distribution of the ESD does not depend on the type of distribution used for the random entries of X_n. We use the universality result to exactly compute the limiting ESD for two families where it was not previously known. The proof of the main result incorporates the Tao-Vu replacement principle and a version of the Lindeberg replacement strategy, along with the newly-defined notion of stability of sets of rows of a matrix.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"45 1","pages":"1877-1896"},"PeriodicalIF":1.5,"publicationDate":"2014-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85485984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 11
Martingale defocusing and transience of a self-interacting random walk 鞅散焦和自相互作用随机漫步的瞬态
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-03-06 DOI: 10.1214/14-AIHP667
Y. Peres, Bruno Schapira, Perla Sousi
{"title":"Martingale defocusing and transience of a self-interacting random walk","authors":"Y. Peres, Bruno Schapira, Perla Sousi","doi":"10.1214/14-AIHP667","DOIUrl":"https://doi.org/10.1214/14-AIHP667","url":null,"abstract":"Suppose that (X;Y;Z) is a random walk in Z 3 that moves in the following way: on the rst visit to a vertex only Z changes by 1 equally likely, while on later visits to the same vertex (X;Y ) performs a two-dimensional random walk step. We show that this walk is transient thus answering a question of Benjamini, Kozma and Schapira. One important ingredient of the proof is a dispersion result for martingales.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"6 1","pages":"1009-1022"},"PeriodicalIF":1.5,"publicationDate":"2014-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75149642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 6
A parametrix approach for some degenerate stable driven SDEs 一类退化稳定驱动SDEs的参数化方法
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-02-17 DOI: 10.1214/15-AIHP704
Lorick Huang, S. Menozzi
{"title":"A parametrix approach for some degenerate stable driven SDEs","authors":"Lorick Huang, S. Menozzi","doi":"10.1214/15-AIHP704","DOIUrl":"https://doi.org/10.1214/15-AIHP704","url":null,"abstract":"We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak Hormander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"87 1","pages":"1925-1975"},"PeriodicalIF":1.5,"publicationDate":"2014-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81343791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 25
Scaling limits of k-ary growing trees k-ary生长树的缩放极限
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-02-05 DOI: 10.1214/14-AIHP622
Bénédicte Haas, R. Stephenson
{"title":"Scaling limits of k-ary growing trees","authors":"Bénédicte Haas, R. Stephenson","doi":"10.1214/14-AIHP622","DOIUrl":"https://doi.org/10.1214/14-AIHP622","url":null,"abstract":"Pour chaque entier k≥2, on introduit une suite d’arbres discrets k-aires construite recursivement en choisissant a chaque etape une arete uniformement parmi les aretes de l’arbre pre-existant et greffant sur son « milieu » k−1 nouvelles aretes. Lorsque k=2, cette procedure correspond a un algorithme introduit par Remy. Pour chaque entier k≥2, nous decrivons la limite d’echelle de ces arbres lorsque le nombre d’etapes n tend vers l’infini : ils grandissent a la vitesse n1/k vers un arbre reel aleatoire k-aire qui appartient a la famille des arbres de fragmentation auto-similaires. Cette convergence a lieu en probabilite, pour la topologie de Gromov–Hausdorff–Prokhorov. Nous etudions egalement l’emboitement des arbres limites quand k varie.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"58 1","pages":"1314-1341"},"PeriodicalIF":1.5,"publicationDate":"2014-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83952474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 14
A geometric approach to correlation inequalities in the plane 平面上相关不等式的几何方法
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-02-01 DOI: 10.1214/12-AIHP494
A. Figalli, F. Maggi, A. Pratelli
{"title":"A geometric approach to correlation inequalities in the plane","authors":"A. Figalli, F. Maggi, A. Pratelli","doi":"10.1214/12-AIHP494","DOIUrl":"https://doi.org/10.1214/12-AIHP494","url":null,"abstract":". By elementary geometric arguments, correlation inequalities for radially symmetric probability measures are proved in the plane. Precisely, it is shown that the correlation ratio for pairs of width-decreasing sets is minimized within the class of infinite strips. Since open convex sets which are symmetric with respect to the origin turn out to be width-decreasing sets, Pitt’s Gaussian correlation inequality (the two-dimensional case of the long-standing Gaussian correlation conjecture) is derived as a corollary, and it is in fact extended to a wide class of radially symmetric measures. Résumé. En utilisant des arguments géométriques élémentaires, on démontre des inégalités de corrélation pour des mesures de probabilité à symétrie radiale. Plus précisément on montre que, parmi la famille des ensembles width-decreasing , le ratio de corrélation est minimisé par des bandes. Comme les ouverts convexes symétriques appartiennent à cette famille, on retrouve comme corollaire le résultat de Pitt sur la validité de la conjecture de corrélation gaussiennne en dimension 2, qui est étendue dans ce papier à une large classe de mesures à symétrie radiale.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"53 6 1","pages":"1-14"},"PeriodicalIF":1.5,"publicationDate":"2014-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83228171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Geodesics in Brownian surfaces (Brownian maps) 布朗曲面中的测地线(布朗图)
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-01-15 DOI: 10.1214/14-AIHP666
Jérémie Bettinelli
{"title":"Geodesics in Brownian surfaces (Brownian maps)","authors":"Jérémie Bettinelli","doi":"10.1214/14-AIHP666","DOIUrl":"https://doi.org/10.1214/14-AIHP666","url":null,"abstract":"We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These spaces generalize the well-known Brownian map and our results generalize the properties shown by Le Gall on geodesics in the latter space. We use a different approach based on two ingredients: we first study typical geodesics and then all geodesics by an ''entrapment'' strategy. Our results give geometrical characterizations of some subsets of interest, in terms of geodesics, boundary points and concatenations of geodesics that are not homotopic to 0.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"7 1","pages":"612-646"},"PeriodicalIF":1.5,"publicationDate":"2014-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83898202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 22
Adaptive pointwise estimation of conditional density function 条件密度函数的自适应点估计
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2013-12-28 DOI: 10.1214/14-AIHP665
K. Bertin, C. Lacour, V. Rivoirard
{"title":"Adaptive pointwise estimation of conditional density function","authors":"K. Bertin, C. Lacour, V. Rivoirard","doi":"10.1214/14-AIHP665","DOIUrl":"https://doi.org/10.1214/14-AIHP665","url":null,"abstract":"In this paper we consider the problem of estimating $f$, the conditional density of $Y$ given $X$, by using an independent sample distributed as $(X,Y)$ in the multivariate setting. We consider the estimation of $f(x,.)$ where $x$ is a fixed point. We define two different procedures of estimation, the first one using kernel rules, the second one inspired from projection methods. Both adapted estimators are tuned by using the Goldenshluger and Lepski methodology. After deriving lower bounds, we show that these procedures satisfy oracle inequalities and are optimal from the minimax point of view on anisotropic Holder balls. Furthermore, our results allow us to measure precisely the influence of $mathrm{f}_X(x)$ on rates of convergence, where $mathrm{f}_X$ is the density of $X$. Finally, some simulations illustrate the good behavior of our tuned estimates in practice.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"40 1","pages":"939-980"},"PeriodicalIF":1.5,"publicationDate":"2013-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81136973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 34
PATHWISE SOLVABILITY OF STOCHASTIC INTEGRAL EQUATIONS WITH GENERALIZED DRIFT AND NON-SMOOTH DISPERSION FUNCTIONS 具有广义漂移和非光滑色散函数的随机积分方程的路径可解性
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2013-12-27 DOI: 10.1214/14-AIHP660
I. Karatzas, J. Ruf
{"title":"PATHWISE SOLVABILITY OF STOCHASTIC INTEGRAL EQUATIONS WITH GENERALIZED DRIFT AND NON-SMOOTH DISPERSION FUNCTIONS","authors":"I. Karatzas, J. Ruf","doi":"10.1214/14-AIHP660","DOIUrl":"https://doi.org/10.1214/14-AIHP660","url":null,"abstract":"We study one-dimensional stochastic integral equations with non-smooth dispersion coefficients, and with drift components that are not restricted to be absolutely continuous with respect to Lebesgue measure. In the spirit of Lamperti, Doss and Sussmann, we relate solutions of such equations to solutions of certain ordinary integral equations, indexed by a generic element of the underlying probability space. This relation allows us to solve the stochastic integral equations in a pathwise sense.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"113 1","pages":"915-938"},"PeriodicalIF":1.5,"publicationDate":"2013-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76070873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 6
Strong stationary times for one-dimensional diffusions 一维扩散的强平稳时间
IF 1.5 2区 数学
Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2013-11-25 DOI: 10.1214/16-aihp745
L. Miclo
{"title":"Strong stationary times for one-dimensional diffusions","authors":"L. Miclo","doi":"10.1214/16-aihp745","DOIUrl":"https://doi.org/10.1214/16-aihp745","url":null,"abstract":"A necessary and sufficient condition is obtained for the existence of strong stationary times for ergodic one-dimensional diffusions, whatever the initial distribution. The strong stationary times are constructed through intertwinings with dual processes, in the Diaconis-Fill sense, taking values in the set of segments of the extended line $mathbb{R}sqcup{-infty,+infty}$. They can be seen as natural $h$-transforms of the extensions to the diffusion framework of the evolving sets of Morris-Peres. Starting from a singleton set, the dual process begins by evolving into true segments in the same way a Bessel process of dimension 3 escapes from 0. The strong stationary time corresponds to the first time the full segment $[-infty,+infty]$ is reached. The benchmark Ornstein-Uhlenbeck process cannot be treated in this way, it will nevertheless be seen how to use other strong times to recover its optimal exponential rate of convergence in the total variation sense.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"1 1","pages":"957-996"},"PeriodicalIF":1.5,"publicationDate":"2013-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79807977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 15
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