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Annales de l Institut Henri Poincare D最新文献

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Couplings for Andersen dynamics 安德森动力学的耦合
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-29 DOI: 10.1214/21-AIHP1197
Nawaf Bou-Rabee, A. Eberle
{"title":"Couplings for Andersen dynamics","authors":"Nawaf Bou-Rabee, A. Eberle","doi":"10.1214/21-AIHP1197","DOIUrl":"https://doi.org/10.1214/21-AIHP1197","url":null,"abstract":"Andersen dynamics is a standard method for molecular simulations, and a precursor of the Hamiltonian Monte Carlo algorithm used in MCMC inference. The stochastic process corresponding to Andersen dynamics is a PDMP (piecewise deterministic Markov process) that iterates between Hamiltonian flows and velocity randomizations of randomly selected particles. Both from the viewpoint of molecular dynamics and MCMC inference, a basic question is to understand the convergence to equilibrium of this PDMP particularly in high dimension. Here we present couplings to obtain sharp convergence bounds in the Wasserstein sense that do not require global convexity of the underlying potential energy.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80763134","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: 8
An upper bound on the two-arms exponent for critical percolation on Zd Zd上临界渗流双臂指数的上界
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-28 DOI: 10.1214/21-aihp1153
J. Berg, Diederik van Engelenburg
{"title":"An upper bound on the two-arms exponent for critical percolation on Zd","authors":"J. Berg, Diederik van Engelenburg","doi":"10.1214/21-aihp1153","DOIUrl":"https://doi.org/10.1214/21-aihp1153","url":null,"abstract":"Consider critical site percolation on $mathbb{Z}^d$ with $d geq 2$. Cerf (2015) pointed out that from classical work by Aizenman, Kesten and Newman (1987) and Gandolfi, Grimmett and Russo (1988) one can obtain that the two-arms exponent is at least $1/2$. The paper by Cerf slightly improves that lower bound. \u0000Except for $d=2$ and for high $d$, no upper bound for this exponent seems to be known in the literature so far (not even implicity). We show that the distance-$n$ two-arms probability is at least $c n^{-(d^2 + 4 d -2)}$ (with $c >0$ a constant which depends on $d$), thus giving an upper bound $d^2 + 4 d -2$ for the above mentioned exponent.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85685333","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
A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group 一般线性群上随机游走系数的一个局部极限定理和不变测度的一个0 - 1定律
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-24 DOI: 10.1214/21-aihp1221
I. Grama, Jean-François Quint, Hui Xiao
{"title":"A zero-one law for invariant measures and a local limit theorem for coefficients of random walks on the general linear group","authors":"I. Grama, Jean-François Quint, Hui Xiao","doi":"10.1214/21-aihp1221","DOIUrl":"https://doi.org/10.1214/21-aihp1221","url":null,"abstract":"We prove a zero-one law for the stationary measure for algebraic sets generalizing the results of Furstenberg [13] and Guivarc'h and Le Page [20]. As an application, we establish a local limit theorem for the coefficients of random walks on the general linear group.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81579743","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
Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential 具有白噪声势的二维抛物型Anderson模型的长期渐近性
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-24 DOI: 10.1214/21-aihp1215
W. Konig, Nicolas Perkowski, W. V. Zuijlen
{"title":"Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential","authors":"W. Konig, Nicolas Perkowski, W. V. Zuijlen","doi":"10.1214/21-aihp1215","DOIUrl":"https://doi.org/10.1214/21-aihp1215","url":null,"abstract":"We consider the parabolic Anderson model (PAM) $partial_t u = frac12 Delta u + xi u$ in $mathbb R^2$ with a Gaussian (space) white-noise potential $xi$. We prove that the almost-sure large-time asymptotic behaviour of the total mass at time $t$, written $U(t)$, is given by $log U(t)sim chi t log t$, with the deterministic constant $chi$ identified in terms of a variational formula. In earlier work of one of the authors this constant was used to describe the asymptotic behaviour principal Dirichlet of the eigenvalue $boldsymbol lambda_1(Q_t)$ of the Anderson operator on the box $Q_t= [-frac{t}{2},frac{t}{2}]^2$ by $boldsymbol lambda_1(Q_t)simchilog t$.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75610413","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: 13
Duality and bicrystals on infinite binary matrices 无限二元矩阵上的对偶性和双晶
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-22 DOI: 10.4171/aihpd/165
Thomas Gerber, C. Lecouvey
{"title":"Duality and bicrystals on infinite binary matrices","authors":"Thomas Gerber, C. Lecouvey","doi":"10.4171/aihpd/165","DOIUrl":"https://doi.org/10.4171/aihpd/165","url":null,"abstract":"The set of finite binary matrices of a given size is known to carry a finite type A bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums together with a natural generalisation of the 2M − X Pitman transform. Next, we show that, once the relevant formalism on families of infinite binary matrices is introduced, this is a particular case of a much more general phenomenon. Each such family of matrices is proved to be endowed with Kac-Moody bicrystal and tricrystal structures defined from the classical root systems. Moreover, we give an explicit decomposition of these multicrystals, reminiscent of the decomposition of characters yielding the Cauchy identities.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89038426","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
Stochastic homogenization of random walks on point processes 点过程随机游走的随机均匀化
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-17 DOI: 10.1214/22-aihp1269
A. Faggionato
{"title":"Stochastic homogenization of random walks on point processes","authors":"A. Faggionato","doi":"10.1214/22-aihp1269","DOIUrl":"https://doi.org/10.1214/22-aihp1269","url":null,"abstract":"We consider random walks on the support of a random purely atomic measure on $mathbb{R}^d$ with random jump probability rates. The jump range can be unbounded. The purely atomic measure is reversible for the random walk and stationary for the action of the group $mathbb{G}=mathbb{R}^d$ or $mathbb{G}=mathbb{Z}^d$. By combining two-scale convergence and Palm theory for $mathbb{G}$-stationary random measures and by developing a cut-off procedure, under suitable second moment conditions we prove for almost all environments the homogenization for the massive Poisson equation of the associated Markov generators. In addition, we obtain the quenched convergence of the $L^2$-Markov semigroup and resolvent of the diffusively rescaled random walk to the corresponding ones of the Brownian motion with covariance matrix $2D$. For symmetric jump rates, the above convergence plays a crucial role in the derivation of hydrodynamic limits when considering multiple random walks with site-exclusion or zero range interaction. We do not require any ellipticity assumption, neither non-degeneracy of the homogenized matrix $D$. Our results cover a large family of models, including e.g. random conductance models on $mathbb{Z}^d$ and on general lattices (possibly with long conductances), Mott variable range hopping, simple random walks on Delaunay triangulations, simple random walks on supercritical percolation clusters.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81086418","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: 6
Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy–Widom GOE distribution 带有飘散物的Airy过程、KPZ波动和Tracy-Widom GOE分布的变形
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-16 DOI: 10.1214/21-AIHP1229
Karl Liechty, G. Nguyen, Daniel Remenik
{"title":"Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy–Widom GOE distribution","authors":"Karl Liechty, G. Nguyen, Daniel Remenik","doi":"10.1214/21-AIHP1229","DOIUrl":"https://doi.org/10.1214/21-AIHP1229","url":null,"abstract":"We study the distribution of the supremum of the Airy process with $m$ wanderers minus a parabola, or equivalently the limit of the rescaled maximal height of a system of $N$ non-intersecting Brownian bridges as $Ntoinfty$, where the first $N-m$ paths start and end at the origin and the remaining $m$ go between arbitrary positions. The distribution provides a $2m$-parameter deformation of the Tracy--Widom GOE distribution, which is recovered in the limit corresponding to all Brownian paths starting and ending at the origin. \u0000We provide several descriptions of this distribution function: (i) A Fredholm determinant formula; (ii) A formula in terms of Painleve II functions; (iii) A representation as a marginal of the KPZ fixed point with initial data given as the top path in a stationary system of reflected Brownian motions with drift; (iv) A characterization as the solution of a version of the Bloemendal--Virag PDE (arXiv:1011.1877, arXiv:1109.3704) for spiked Tracy--Widom distributions; (v) A representation as a solution of the KdV equation. We also discuss connections with a model of last passage percolation with boundary sources.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81371283","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: 5
The structure of spatial slices of 3-dimensional causal triangulations 三维因果三角剖分的空间切片结构
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-15 DOI: 10.4171/aihpd/91
B. Durhuus, T. Jonsson
{"title":"The structure of spatial slices of 3-dimensional causal triangulations","authors":"B. Durhuus, T. Jonsson","doi":"10.4171/aihpd/91","DOIUrl":"https://doi.org/10.4171/aihpd/91","url":null,"abstract":". We consider causal 3-dimensional triangulations with the topology of S 2 × [0 , 1] or D 2 × [0 , 1] where S 2 and D 2 are the 2-dimensional sphere and disc, respectively. These triangulations consist of slices and we show that these slices can be mapped bijectively onto a set of certain coloured 2-dimensional cell complexes satisfying simple conditions. The cell complexes arise as the cross section of the individual slices.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91377185","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
Quasi-geometric rough paths and rough change of variable formula 拟几何粗糙路径及变量公式的粗糙变换
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-09-02 DOI: 10.1214/22-aihp1297
C. Bellingeri
{"title":"Quasi-geometric rough paths and rough change of variable formula","authors":"C. Bellingeri","doi":"10.1214/22-aihp1297","DOIUrl":"https://doi.org/10.1214/22-aihp1297","url":null,"abstract":"Using some basic notions from the theory of Hopf algebras and quasi-shuffle algebras, we introduce rigorously a new family of rough paths: the quasi-geometric rough paths. We discuss their main properties. In particular, we will relate them with iterated Brownian integrals and the concept of \"simple bracket extension\", developed in the PhD thesis of David Kelly. As a consequence of these results, we have a sufficient criterion to show for any $gammain (0,1)$ and any sufficiently smooth function $varphi colon mathbb{R}^dto mathbb{R}$ a rough change of variable formula on any $gamma$-Holder continuous path $xcolon [0, T]to mathbb{R}^d$, i.e. an explicit expression of $varphi(x_t)$ in terms of rough integrals.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86614538","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: 5
A simple backward construction of branching Brownian motion with large displacement and applications 大位移分支布朗运动的简单反向构造及其应用
IF 1.5
Annales de l Institut Henri Poincare D Pub Date : 2020-08-31 DOI: 10.1214/21-aihp1212
J. Berestycki, E. Brunet, A. Cortines, Bastien Mallein
{"title":"A simple backward construction of branching Brownian motion with large displacement and applications","authors":"J. Berestycki, E. Brunet, A. Cortines, Bastien Mallein","doi":"10.1214/21-aihp1212","DOIUrl":"https://doi.org/10.1214/21-aihp1212","url":null,"abstract":"In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal processes of several branching processes, including branching Brownian motions with variable speed and multitype branching Brownian motions. We give a new, alternative representation of these point measures and we show that they form a continuous family. This also yields a simple probabilistic expression for the constant that appears in the large deviation probability of having a large displacement. As an application, we show that Bovier and Hartung (2015)'s results about variable speed branching Brownian motion also describe the extremal point process of branching Ornstein-Uhlenbeck processes.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86147811","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: 9
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