Annales de l Institut Henri Poincare D最新文献_第6页

Scaling limit for random walk on the range of random walk in four dimensions 随机行走在四维范围上的缩放限制

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-04-08 DOI: 10.1214/22-aihp1243

D. Croydon, D. Shiraishi

引用次数: 2

Local and global comparisons of the Airy difference profile to Brownian local time 艾里差剖面与布朗地方时的地方和全球比较

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-03-22 DOI: 10.1214/22-aihp1290

S. Ganguly, Milind Hegde

{"title":"Local and global comparisons of the Airy difference profile to Brownian local time","authors":"S. Ganguly, Milind Hegde","doi":"10.1214/22-aihp1290","DOIUrl":"https://doi.org/10.1214/22-aihp1290","url":null,"abstract":"There has recently been much activity within the Kardar-Parisi-Zhang universality class spurred by the construction of the canonical limiting object, the parabolic Airy sheet $mathcal{S}:mathbb{R}^2tomathbb{R}$ [arXiv:1812.00309]. The parabolic Airy sheet provides a coupling of parabolic Airy$_2$ processes -- a universal limiting geodesic weight profile in planar last passage percolation models -- and a natural goal is to understand this coupling. Geodesic geometry suggests that the difference of two parabolic Airy$_2$ processes, i.e., a difference profile, encodes important structural information. This difference profile $mathcal{D}$, given by $mathbb{R}tomathbb{R}:xmapsto mathcal{S}(1,x)- mathcal{S}(-1,x)$, was first studied by Basu, Ganguly, and Hammond [arXiv:1904.01717], who showed that it is monotone and almost everywhere constant, with its points of non-constancy forming a set of Hausdorff dimension $1/2$. Noticing that this is also the Hausdorff dimension of the zero set of Brownian motion leads to the question: is there a connection between $mathcal{D}$ and Brownian local time? Establishing that there is indeed a connection, we prove two results. On a global scale, we show that $mathcal{D}$ can be written as a Brownian local time patchwork quilt, i.e., as a concatenation of random restrictions of functions which are each absolutely continuous to Brownian local time (of rate four) away from the origin. On a local scale, we explicitly obtain Brownian local time of rate four as a local limit of $mathcal{D}$ at a point of increase, picked by a number of methods, including at a typical point sampled according to the distribution function $mathcal{D}$. Our arguments rely on the representation of $mathcal{S}$ in terms of a last passage problem through the parabolic Airy line ensemble and an understanding of geodesic geometry at deterministic and random times.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84301867","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: 11

Short cycles in high genus unicellular maps 高属单细胞图中的短周期

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-03-03 DOI: 10.1214/21-aihp1218

S. Janson, B. Louf

引用次数: 4

Busemann process and semi-infinite geodesics in Brownian last-passage percolation 布朗末道渗流中的Busemann过程和半无限测地线

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-03-01 DOI: 10.1214/22-aihp1245

T. Seppalainen, Evan L. Sorensen

{"title":"Busemann process and semi-infinite geodesics in Brownian last-passage percolation","authors":"T. Seppalainen, Evan L. Sorensen","doi":"10.1214/22-aihp1245","DOIUrl":"https://doi.org/10.1214/22-aihp1245","url":null,"abstract":". We prove the existence of semi-inﬁnite geodesics for Brownian last-passage percolation (BLPP). Speciﬁcally, on a single event of probability one, there exist semi-inﬁnite geodesics started from every space- time point and traveling in every asymptotic direction. Properties of these geodesics include uniqueness for a ﬁxed initial point and direction, non-uniqueness for ﬁxed direction but random initial points, and coalescence of all geodesics traveling in a common, ﬁxed direction. Along the way, we prove that for ﬁxed northeast and southwest directions, there almost surely exist no bi-inﬁnite geodesics in the given directions. The semi-inﬁnite geodesics are constructed from Busemann functions. Our starting point is a result of Alberts, Rassoul-Agha and Simper that established Busemann functions for ﬁxed points and directions. Out of this, we construct the global process of Busemann functions simultaneously for all initial points and directions, and then the family of semi-inﬁnite Busemann geodesics. The uncountable space of the semi-discrete setting requires extra consideration and leads to new phenomena, compared to discrete models.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80724942","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: 10

Negative correlation of adjacent Busemann increments 相邻Busemann增量呈负相关

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-02-12 DOI: 10.1214/21-aihp1236

Ian Alevy, Arjun Krishnan

引用次数: 3

Typicality and entropy of processes on infinite trees 无限树上过程的典型性和熵

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-02-04 DOI: 10.1214/21-aihp1233

'Agnes Backhausz, C. Bordenave, B. Szegedy

引用次数: 5

Continuity in κ in SLEκ theory using a constructive method and Rough Path Theory 基于构造方法和粗糙路径理论的SLEκ理论中κ的连续性

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-02-01 DOI: 10.1214/20-AIHP1084

D. Beliaev, Terry Lyons, Vlad Margarint

{"title":"Continuity in κ in SLEκ theory using a constructive method and Rough Path Theory","authors":"D. Beliaev, Terry Lyons, Vlad Margarint","doi":"10.1214/20-AIHP1084","DOIUrl":"https://doi.org/10.1214/20-AIHP1084","url":null,"abstract":"Questions regarding the continuity in κ of the SLE κ traces and maps appear very naturally in the study of SLE. In order to study the ﬁrst question, we consider a natural coupling of SLE traces: for diﬀerent values of κ we use the same Brownian motion. It is very natural to assume that with probability one, SLE κ depends continuously on κ . It is rather easy to show that SLE is continuous in the Carath´eodory sense, but showing that SLE traces are continuous in the uniform sense is much harder. In this note we show that for a given sequence κ j → κ ∈ (0 , 8 / 3), for almost every Brownian motion SLE κ traces converge locally uniformly. This result was also recently obtained by Friz, Tran and Yuan using diﬀerent methods. In our analysis, we provide a constructive way to study the SLE κ traces for varying parameter κ ∈ (0 , 8 / 3). The argument is based on a new dynamical view on the approximation of SLE curves by curves driven by a piecewise square root approximation of the Brownian motion. The second question can be answered naturally in the framework of Rough Path Theory. Using this theory, we prove that the solutions of the backward Loewner Diﬀerential Equation driven by √ κB t when started away from the origin are continuous in the p -variation topology in the parameter κ , for all κ ∈ R + .","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76064898","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

Erratum: Central limit theorems for eigenvalues in a spiked population model [Annales de l’Institut Henri Poincaré – Probabilités et Statistiques 2008, Vol. 44, No. 3, 447–474] 勘定:尖峰人口模型特征值的中心极限定理[亨利研究所年鉴poincare -概率与统计2008，第44卷，第3期，447 - 474]

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-02-01 DOI: 10.1214/20-aihp1078

Z. Bai, Jianfeng Yao

引用次数: 0

Skorohod and rough integration for stochastic differential equations driven by Volterra processes Volterra过程驱动的随机微分方程的Skorohod和粗糙积分

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-02-01 DOI: 10.1214/20-AIHP1074

T. Cass, Nengli Lim

{"title":"Skorohod and rough integration for stochastic differential equations driven by Volterra processes","authors":"T. Cass, Nengli Lim","doi":"10.1214/20-AIHP1074","DOIUrl":"https://doi.org/10.1214/20-AIHP1074","url":null,"abstract":". Given a solution Y to a rough differential equation (RDE), a recent result ( Ann. Probab. 47 (2019) 1–60) extends the classical Itô-Stratonovich formula and provides a closed-form expression for (cid:2) Y ◦ d X − (cid:2) Y d X , i.e. the difference between the rough and Skorohod integrals of Y with respect to X , where X is a Gaussian process with ﬁnite p -variation less than 3. In this paper, we extend this result to Gaussian processes with ﬁnite p -variation such that 3 ≤ p < 4. The constraint this time is that we restrict ourselves to Volterra Gaussian processes with kernels satisfying a natural condition, which however still allows the result to encompass many standard examples, including fractional Brownian motion with Hurst parameter H > 14 . As an application we recover Itô formulas in the case where the vector ﬁelds of the RDE governing Y are commutative. Résumé. (2019) l’intégrale rugueuse et l’intégrale de Skorohod de Y par rapport à X , où X est un processus Gaussien avec p -variation plus petite que 3. Dans cet article, nous étendons ce résultat au cas de processus Gaussiens avec p -variation telle que 3 ≤ p < 4. La contrainte ici est que nous nous restreignons au cas de processus Gaussiens de type Volterra avec des noyaux satisfaisant une condition naturelle, ce qui permet néanmoins de traiter beaucoup d’exemples classiques incluant le cas du mouvement Brownien fractionnaire avec paramètre de Hurst H > 14 . Comme application, nous retrouvons la formule d’Itô dans le cas où les champs de vecteurs de la RDE gouvernant Y sont commutatifs.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83265718","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

Rates of convergence in the central limit theorem for martingales in the non stationary setting 非平稳条件下鞅中心极限定理的收敛速率

IF 1.5

Annales de l Institut Henri Poincare D Pub Date : 2021-01-18 DOI: 10.1214/21-aihp1182

J. Dedecker, F. Merlevède, E. Rio

引用次数: 8