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Annales de l Institut Henri Poincare D最新文献

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Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations 边界驱动粒子系统的正交多项式对偶性与非平衡相关
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-07-16 DOI: 10.1214/21-aihp1163
Simone Floreani, F. Redig, F. Sau
{"title":"Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations","authors":"Simone Floreani, F. Redig, F. Sau","doi":"10.1214/21-aihp1163","DOIUrl":"https://doi.org/10.1214/21-aihp1163","url":null,"abstract":"We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then we derive new orthogonal polynomial dualities. From the classical dualities, we derive the uniqueness of the non-equilibrium steady state and obtain correlation inequalities. Starting from the orthogonal polynomial dualities, we show universal properties of n-point correlation functions in the non-equilibrium steady state for systems with at most two different reservoir parameters, such as a chain with reservoirs at left and right ends.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"43 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82517985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
Weak convergence of the intersection point process of Poisson hyperplanes 泊松超平面交点过程的弱收敛性
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-07-13 DOI: 10.1214/21-aihp1201
A. Baci, Gilles Bonnet, Christoph Thale
{"title":"Weak convergence of the intersection point process of Poisson hyperplanes","authors":"A. Baci, Gilles Bonnet, Christoph Thale","doi":"10.1214/21-aihp1201","DOIUrl":"https://doi.org/10.1214/21-aihp1201","url":null,"abstract":"This paper deals with the intersection point process of a stationary and isotropic Poisson hyperplane process in $mathbb{R}^d$ of intensity $t>0$, where only hyperplanes that intersect a centred ball of radius $R>0$ are considered. Taking $R=t^{-frac{d}{d+1}}$ it is shown that this point process converges in distribution, as $ttoinfty$, to a Poisson point process on $mathbb{R}^dsetminus{0}$ whose intensity measure has power-law density proportional to $|x|^{-(d+1)}$ with respect to the Lebesgue measure. A bound on the speed of convergence in terms of the Kantorovich-Rubinstein distance is provided as well. In the background is a general functional Poisson approximation theorem on abstract Poisson spaces. Implications on the weak convergence of the convex hull of the intersection point process and the convergence of its $f$-vector are also discussed, disproving and correcting thereby a conjecture of Devroye and Toussaint [J. Algorithms 14.3 (1993), 381--394] in computational geometry.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"31 2 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83105844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Quenched invariance principle for long range random walks in balanced random environments 平衡随机环境下长距离随机行走的淬灭不变性原理
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-07-07 DOI: 10.1214/21-aihp1150
Xin Chen, Zhen-Qing Chen, T. Kumagai, Jian Wang
{"title":"Quenched invariance principle for long range random walks in balanced random environments","authors":"Xin Chen, Zhen-Qing Chen, T. Kumagai, Jian Wang","doi":"10.1214/21-aihp1150","DOIUrl":"https://doi.org/10.1214/21-aihp1150","url":null,"abstract":"We establish via a probabilistic approach the quenched invariance principle for a class of long range random walks in independent (but not necessarily identically distributed) balanced random environments, with the transition probability from $x$ to $y$ on average being comparable to $|x-y|^{-(d+alpha)}$ with $alphain (0,2]$. We use the martingale property to estimate exit time from balls and establish tightness of the scaled processes, and apply the uniqueness of the martingale problem to identify the limiting process. When $alphain (0,1)$, our approach works even for non-balanced cases. When $alpha=2$, under a diffusive with the logarithmic perturbation scaling, we show that the limit of scaled processes is a Brownian motion.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"20 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88974447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential 随机势中随机游走的猝灭Lyapunov指数的一个形状定理和变分公式
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-06-18 DOI: 10.1214/21-aihp1200
Christopher Janjigian, Sergazy Nurbavliyev, F. Rassoul-Agha
{"title":"A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential","authors":"Christopher Janjigian, Sergazy Nurbavliyev, F. Rassoul-Agha","doi":"10.1214/21-aihp1200","DOIUrl":"https://doi.org/10.1214/21-aihp1200","url":null,"abstract":"We prove a shape theorem and derive a variational formula for the limiting quenched Lyapunov exponent and the Green's function of random walk in a random potential on a square lattice of arbitrary dimension and with an arbitrary finite set of steps. The potential is a function of a stationary environment and the step of the walk. This potential is subject to a moment assumption whose strictness is tied to the mixing of the environment. Our setting includes directed and undirected polymers, random walk in static and dynamic random environment, and, when the temperature is taken to zero, our results also give a shape theorem and a variational formula for the time constant of both site and edge directed last-passage percolation and standard first-passage percolation.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"18 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83302210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Variance linearity for real Gaussian zeros 实高斯零的方差线性
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-06-17 DOI: 10.1214/21-aihp1228
R. Lachièze-Rey
{"title":"Variance linearity for real Gaussian zeros","authors":"R. Lachièze-Rey","doi":"10.1214/21-aihp1228","DOIUrl":"https://doi.org/10.1214/21-aihp1228","url":null,"abstract":"We investigate the zero set of a stationary Gaussian process on the real line, and in particular give lower bounds for the variance of the number of points on a large interval, in all generality. We prove that this point process is never hyperuniform, i.e. the variance is at least linear, and give necessary conditions to have linear variance, which are close to be sharp. We study the class of symmetric Bernoulli convolutions and give an example where the zero set is super rigid, weakly mixing, and not hyperuniform.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"48 8 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81732832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Logarithmic correction to resistance 对阻力的对数修正
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-06-06 DOI: 10.1214/21-aihp1213
Antal A. J'arai, Dante Mata L'opez
{"title":"Logarithmic correction to resistance","authors":"Antal A. J'arai, Dante Mata L'opez","doi":"10.1214/21-aihp1213","DOIUrl":"https://doi.org/10.1214/21-aihp1213","url":null,"abstract":"We study the trace of the incipient infinite oriented branching random walk in $mathbb{Z}^d times mathbb{Z}_+$ when the dimension is $d = 6$. Under suitable moment assumptions, we show that the electrical resistance between the root and level $n$ is $O(n log^{-xi}n )$ for a $xi > 0$ that does not depend on details of the model.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"23 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78190559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Izergin-Korepin analysis on the wavefunctions of the $U_q(mathrm {sl}_2)$ six-vertex model with reflecting end 具有反射端$U_q( mathm {sl}_2)$六顶点模型的波函数Izergin-Korepin分析
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-06-05 DOI: 10.4171/AIHPD/83
K. Motegi
{"title":"Izergin-Korepin analysis on the wavefunctions of the $U_q(mathrm {sl}_2)$ six-vertex model with reflecting end","authors":"K. Motegi","doi":"10.4171/AIHPD/83","DOIUrl":"https://doi.org/10.4171/AIHPD/83","url":null,"abstract":"We extend the recently developed Izergin-Korepin analysis on the wavefunctions of the $U_q(sl_2)$ six-vertex model to the reflecting boundary conditions. Based on the Izergin-Korepin analysis, we determine the exact forms of the symmetric functions which represent the wavefunctions and its dual. Comparison of the symmetric functions with the coordinate Bethe ansatz wavefunctions for the open XXZ chain by Alcaraz-Barber-Batchelor-Baxter-Quispel is also made. As an application, we derive algebraic identities for the symmetric functions by combining the results with the determinant formula of the domain wall boundary partition function of the six-vertex model with reflecting end.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"46 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74076780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Edwards–Wilkinson fluctuations for the directed polymer in the full L2-regime for dimensions d≥3 d≥3维的定向聚合物在全l2区中的edward - wilkinson波动
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-05-26 DOI: 10.1214/21-aihp1173
Dimitris Lygkonis, Nikos Zygouras
{"title":"Edwards–Wilkinson fluctuations for the directed polymer in the full L2-regime for dimensions d≥3","authors":"Dimitris Lygkonis, Nikos Zygouras","doi":"10.1214/21-aihp1173","DOIUrl":"https://doi.org/10.1214/21-aihp1173","url":null,"abstract":"We prove that in the full $L^2$-regime the partition function of the directed polymer model in dimensions $dgeq 3$, if centered, scaled and averaged with respect to a test function $varphi in C_c(mathbb{R}^d)$, converges in distribution to a Gaussian random variable with explicit variance. Introducing a new idea in this context of a martingale difference representation, we also prove that the log-partition function, which can be viewed as a discretisation of the KPZ equation, exhibits the same fluctuations, when centered and averaged with respect to a test function. Thus, the two models fall within the Edwards-Wilkinson universality class in the full $L^2$-regime, a result that was only established, so far, for a strict subset of this regime in $dgeq 3$.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"14 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80399841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
A central limit theorem for descents of a Mallows permutation and its inverse Mallows置换及其逆的下降的中心极限定理
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-05-20 DOI: 10.1214/21-AIHP1167
Jimmy He
{"title":"A central limit theorem for descents of a Mallows permutation and its inverse","authors":"Jimmy He","doi":"10.1214/21-AIHP1167","DOIUrl":"https://doi.org/10.1214/21-AIHP1167","url":null,"abstract":"This paper studies the asymptotic distribution of descents $des(w)$ in a permutation $w$, and its inverse, distributed according to the Mallows measure. The Mallows measure is a non-uniform probability measure on permutations introduced to study ranked data. Under this measure, permutations are weighted according to the number of inversions they contain, with the weighting controlled by a parameter $q$. The main results are a Berry-Esseen theorem for $des(w)+des(w^{-1})$ as well as a joint central limit theorem for $(des(w),des(w^{-1}))$ to a bivariate normal with a non-trivial correlation depending on $q$. The proof uses Stein's method with size-bias coupling along with a regenerative process associated to the Mallows measure.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"25 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80099646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
Large deviation principle for the intersection measure of Brownian motions on unbounded domains 无界域上布朗运动交点测量的大偏差原理
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-05-19 DOI: 10.1214/22-aihp1244
T. Mori
{"title":"Large deviation principle for the intersection measure of Brownian motions on unbounded domains","authors":"T. Mori","doi":"10.1214/22-aihp1244","DOIUrl":"https://doi.org/10.1214/22-aihp1244","url":null,"abstract":"Consider the intersection measure $ell^{mathrm{IS}}_t$ of $p$ independent Brownian motions on $mathbb{R}^d$. In this article, we prove the large deviation principle for the normalized intersection measure $t^{-p}ell^{mathrm{IS}}_t$ as $trightarrow infty$, before exiting a (possibly unbounded) domain $Dsubsetmathbb{R}^d$ with smooth boundary. This is an extension of [W. Konig and C. Mukherjee: Communications on Pure and Applied Mathematics, 66(2):263--306, 2013] which deals with the case $D$ is bounded. Our essential contribution is to prove the so-called super-exponential estimate for the intersection measure of killed Brownian motions on such $D$ by an application of the Chapman-Kolmogorov relation.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75613995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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