Annales De L Institut Henri Poincare-probabilites Et Statistiques最新文献_第3页

Directed polymer in γ-stable random environments 定向聚合物在γ稳定随机环境中的应用

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2021-05-01 DOI: 10.1214/20-AIHP1108

Robert D. Viveros

{"title":"Directed polymer in γ-stable random environments","authors":"Robert D. Viveros","doi":"10.1214/20-AIHP1108","DOIUrl":"https://doi.org/10.1214/20-AIHP1108","url":null,"abstract":"The transition from a weak-disorder (diffusive) to a strong-disorder (localized) phase for directed polymers in a random environment is a well studied phenomenon. In the most common setup, it is established that the phase transition is trivial when the transversal dimension d equals 1 or 2 (the diffusive phase is reduced to β=0) while when d≥3, there is a critical temperature βc∈(0,∞) which delimits the two phases. The proof of the existence of a diffusive regime for d≥3 is based on a second moment method (Comm. Math. Phys. 123 (1989) 529–534, Ann. Probab. 34 (2006) 1746–1770, J. Stat. Phys. 52 (1988) 609–626), and thus relies heavily on the assumption that the variable which encodes the disorder intensity (which in most of the mathematics literature assumes the form eβηx), has finite second moment. The aim of this work is to investigate how the presence/absence of phase transition may depend on the dimension d in the case when the disorder variable displays a heavier tail. To this end we replace eβηx by (1+βωx) where ωx is in the domain of attraction of a stable law with parameter γ∈(1,2). In this setup we show that a non-trivial phase transition occurs if and only if γ>1+2/d. More precisely, when γ≤1+2/d, the free energy of the system is smaller than its annealed counterpart at every temperature whereas when γ>1+2/d the martingale sequence of renormalized partition functions converges to an almost surely positive random variable for all β sufficiently small.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"5 1","pages":"1081-1102"},"PeriodicalIF":1.5,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74959065","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

Two-temperatures overlap distribution for the 2D discrete Gaussian free field 二维离散高斯自由场的双温度重叠分布

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2021-05-01 DOI: 10.1214/20-AIHP1091

Michel Pain, Olivier Zindy

引用次数: 2

Gaussian fluctuations for the directed polymer partition function in dimension d≥3 and in the whole L2-region 定向聚合物配分函数在d≥3维和整个l2区域的高斯波动

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2021-05-01 DOI: 10.1214/20-AIHP1100

Clément Cosco, S. Nakajima

引用次数: 4

The Schelling model on Z 关于Z的谢林模型

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2021-05-01 DOI: 10.1214/20-AIHP1096

Maria Deijfen, Timo Vilkas

引用次数: 0

Estimating a density, a hazard rate, and a transition intensity via the ρ-estimation method 通过ρ估计方法估计密度、危险率和过渡强度

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2021-02-01 DOI: 10.1214/20-AIHP1076

M. Sart

引用次数: 0

Global observables for RW: Law of large numbers RW的全局观测:大数定律

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2021-02-01 DOI: 10.1214/20-AIHP1072

D. Dolgopyat, M. Lenci, Péter Nándori

引用次数: 4

Hausdorff dimension of the uniform measure of Galton–Watson trees without the XlogX condition 不带XlogX条件的高尔顿-沃森树的均匀测度的豪斯多夫维数

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2020-11-01 DOI: 10.1214/19-aihp1031

EF Elie Aidékon

引用次数: 0

Obliquely reflected backward stochastic differential equations 斜反射后向随机微分方程

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2020-11-01 DOI: 10.1214/20-aihp1061

J. Chassagneux, A. Richou

引用次数: 7

Superdiffusions with super-exponential growth: Construction, mass and spread 具有超指数增长的超扩散:结构、质量和扩散

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2020-08-01 DOI: 10.1214/19-aihp1018

Zhen-Qing Chen, J. Engländer

{"title":"Superdiffusions with super-exponential growth: Construction, mass and spread","authors":"Zhen-Qing Chen, J. Engländer","doi":"10.1214/19-aihp1018","DOIUrl":"https://doi.org/10.1214/19-aihp1018","url":null,"abstract":"Superdi usions corresponding to di erential operators of the form Lu+βu−αu with mass creation (potential) terms β(·) that are `large functions' are studied. Our construction for superdi usions with large mass creations works for the branching mechanism βu−αu , 0 < γ < 1, as well. Let D ⊆ R be a domain in R. When β is large, the generalized principal eigenvalue λc of L+β in D is typically in nite. Let {Tt, t ≥ 0} denote the Schrödinger semigroup of L + β in D with zero Dirichlet boundary condition. Under the mild assumption that there exists an 0 < h ∈ C(D) so that Tth is nite-valued for all t ≥ 0, we show that there is a uniqueMloc(D)-valued Markov process that satis es a log-Laplace equation in terms of the minimal nonnegative solution to a semilinear initial value problem. Although for super-Brownian motion (SBM) this assumption requires β to be less than quadratic, the quadratic case will be treated as well. When λc = ∞, the usual machinery, including martingale methods and PDE as well as other similar techniques cease to work e ectively, both for the construction and for the investigation of the large time behavior of superdi usions. In this paper, we develop the following two new techniques for the study of the local/global growth of mass and for the spread of superdi usions: • a generalization of the Fleischmann-Swart `Poisson-coupling,' linking superprocesses with branching di usions; • the introduction of a new concept: the `p-generalized principal eigenvalue.' The precise growth rate for the total population of SBM with α(x) = β(x) = 1 + |x| for p ∈ [0, 2] is given in this paper.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"1 1","pages":"1809-1840"},"PeriodicalIF":1.5,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87634081","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: 0

Stochastic Hölder continuity of random fields governed by a system of stochastic PDEs 随机Hölder由随机偏微分方程系统控制的随机场的连续性

IF 1.5 2区数学

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2020-05-01 DOI: 10.1214/19-aihp1000

Kai Du, Jiakun Liu, Fu Zhang

引用次数: 3