Annales Henri Lebesgue最新文献

{"title":"Asymptotic shape of the concave majorant of a Lévy process","authors":"D. Bang, Jorge Ignacio Gonz'alez C'azares, Aleksandar Mijatovi'c","doi":"10.5802/ahl.136","DOIUrl":"https://doi.org/10.5802/ahl.136","url":null,"abstract":". — We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value at T ) of a Lévy process on [0 , T ] as T → ∞ . The scale of the fluctuations of the length and other statistics, as well as their asymptotic dependence, vary significantly with the tail behaviour of the Lévy measure. The key tool in the proofs is the recent representation of the concave majorant for all Lévy processes using a stick-breaking representation. Résumé. — Nous établissons des théorèmes distributionnels limites pour les statistiques de la forme d’un majorant concave (i.e. les fluctuations de sa longueur, son supremum, son temps d’atteinte et sa valeur en T ) d’un processus de Lévy sur [0 , T ] lorsque T → ∞ . L’ampleur des","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"199 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126363795","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}

{"title":"Triangulations of uniform subquadratic growth are quasi-trees","authors":"I. Benjamini, Agelos Georgakopoulos","doi":"10.5802/ahl.139","DOIUrl":"https://doi.org/10.5802/ahl.139","url":null,"abstract":". — It is known that for every α (cid:62) 1 there is a planar triangulation in which every ball of radius r has size Θ( r α ). We prove that for α < 2 every such triangulation is quasi-isometric to a tree. The result extends to Riemannian 2-manifolds of finite genus, and to large-scale-simply-connected graphs. We also prove that every planar triangulation of asymptotic dimension 1 is quasi-isometric to a tree. Résumé. — On sait que pour tout α (cid:62) 1 il existe une triangulation planaire dans laquelle toute boule de rayon r a une taille Θ( r α ). Nous prouvons que pour α < 2 une telle triangulation est quasi-isométrique à un arbre. Le résultat s’étend aux 2-variétés riemanniennes de genre fini, et aux graphes simplement connexes à grande échelle. Nous prouvons également que toute triangulation planaire de dimension asymptotique 1 est quasi-isométrique à un arbre.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115780833","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}

{"title":"Borel fractional colorings of Schreier graphs","authors":"Anton Bernshteyn","doi":"10.5802/ahl.145","DOIUrl":"https://doi.org/10.5802/ahl.145","url":null,"abstract":". Let Γ be a countable group and let G be the Schreier graph of the free part of the Bernoulli shift Γ ý 2 Γ (with respect to some finite subset F Ď Γ). We show that the Borel fractional chromatic number of G is equal to 1 over the measurable independence number of G . As a consequence, we asymptotically determine the Borel fractional chromatic number of G when Γ is the free group, answering a question of Meehan.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132103206","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}

{"title":"Sharp phase transition for Gaussian percolation in all dimensions","authors":"Franco Severo","doi":"10.5802/ahl.141","DOIUrl":"https://doi.org/10.5802/ahl.141","url":null,"abstract":". — We consider the level-sets of continuous Gaussian fields on R d above a certain level − ‘ ∈ R , which defines a percolation model as ‘ varies. We assume that the covariance kernel satisfies certain regularity, symmetry and positivity conditions as well as a polynomial decay with exponent greater than d (in particular, this includes the Bargmann–Fock field). Under these assumptions, we prove that the model undergoes a sharp phase transition around its critical point ‘ c . More precisely, we show that connection probabilities decay exponentially for ‘ < ‘ c and percolation occurs in sufficiently thick 2D slabs for ‘ > ‘ c . This extends results recently obtained in dimension d = 2 to arbitrary dimensions through completely different techniques. The result follows from a global comparison with a truncated (i.e. with finite range of dependence) and discretized (i.e. defined on the lattice ε Z d ) version of the model, which may be of independent interest. The proof of this comparison relies on an interpolation scheme that integrates out the long-range and infinitesimal correlations of the model while compensating them with a slight change in the parameter ‘ . Résumé. — On considère les courbes de niveau de champs gaussiens continus sur R d au-dessus d’un certain niveau − ‘ ∈ R , ce qui définit un modèle de percolation lorsque ‘ varie. Nous supposons que le noyau de covariance satisfait certaines conditions de régularité, de symétrie et de positivité ainsi qu’une décroissance polynomiale d’exposant supérieur à d (cela inclut notamment le champ de Bargmann–Fock). Sous ces hypothèses, nous prouvons que le modèle subit une transition de phase abrupte autour de son point critique ‘ c . Plus précisément, nous montrons que les probabilités de connexion décroissent exponentiellement pour ‘ < ‘ c et que la percolation se produit dans des dalles 2D suffisamment épaisses pour ‘ > ‘ c . Ceci étenddles résultats récemment obtenus en dimension d = 2 à des dimensions arbitraires par des techniques complètement différentes. Le résultat découle d’une comparaison globale avec une version tronquée (c’est-à-dire avec une plage de dépendance finie) et discrétisée (c’est-à-dire définie sur le réseau ε Z d ) du modèle, qui peut présenter un intérêt indépendant. La démonstration de cette comparaison repose sur un schéma d’interpolation qui intègre les corrélations à longue portée et infinitésimales du modèle tout en les compensant par une légère modification du paramètre ‘ .","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127220539","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}

{"title":"Poisson process approximation under stabilization and Palm coupling","authors":"O. Bobrowski, Matthias Schulte, D. Yogeshwaran","doi":"10.5802/ahl.156","DOIUrl":"https://doi.org/10.5802/ahl.156","url":null,"abstract":". — We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic geometry. Our bounds are derived for the Kantorovich–Rubinstein distance using the generator approach to","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122515419","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}

{"title":"Dynamics of lineages in adaptation to a gradual environmental change","authors":"V. Calvez, Benoît Henry, S. M'el'eard, V. Tran","doi":"10.5802/ahl.135","DOIUrl":"https://doi.org/10.5802/ahl.135","url":null,"abstract":"We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by the adaptation to the varying environment. The individuals are characterized by a one-dimensional trait. The dynamics -births and deathsdepend on a time-changing mortality rate that shifts the optimal trait to the right at constant speed. The population size is regulated by a nonlinear non-local logistic competition term. The macroscopic behaviour can be described by a PDE that admits a unique positive stationary solution. In the stationary regime, the population can persist, but with a lag in the trait distribution due to the environmental change. For the microscopic (individual-based) stochastic process, the evolution of the lineages can be traced back using the historical process, that is, a measure-valued process on the set of continuous real functions of time. Assuming stationarity of the trait distribution, we describe the limiting distribution, in large populations, of the path of an individual drawn at random at a given time T . Freezing the non-linearity due to competition allows the use of a many-to-one identity together with Feynman-Kac’s formula. This path, in reversed time, remains close to a simple Ornstein-Uhlenbeck process. It shows how the lagged bulk of the present population stems from ancestors once optimal in trait but still in the tail of the trait distribution in which they lived.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127010779","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}

{"title":"Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants","authors":"J. Bouttier, E. Guitter, G. Miermont","doi":"10.5802/ahl.143","DOIUrl":"https://doi.org/10.5802/ahl.143","url":null,"abstract":"— We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by Collet and Fusy. In this paper, we obtain an even simpler formula for tight pairs of pants, namely for maps whose boundaries have minimal length in their homotopy class. We follow a bijective approach based on the slice decomposition, which we extend by introducing new fundamental building blocks called bigeodesic triangles and diangles, and by working on the universal cover of the triply punctured sphere. We also discuss the statistics of the lengths of minimal separating loops in (non necessarily tight) pairs of pants and annuli, and their asymptotics in the large volume limit. Résumé. — Nous considérons des cartes planaires à trois bords, plus familièrement appelées «pantalons». Dans le cas de cartes biparties avec un contrôle sur le degré des faces, une expression simple pour leur fonction génératrice a été trouvée par Eynard et prouvée bijectivement par Collet et Fusy. Dans cet article nous obtenons une formule encore plus simple pour les pantalons serrés, c’est-à-dire pour les cartes dont les bords ont une longueur minimale dans leur classe d’homotopie. Nous utilisons une approche bijective basée sur la décomposition en tranches, que nous étendons en introduisant de nouveaux blocs fondamentaux appelés triangles et diangles bigéodésiques, et en travaillant sur le revêtement universel de la sphère à trois trous. Nous discutons également la statistique des longueurs minimales des boucles séparantes au sein des pantalons et des cartes annulaires (non nécessairement serrés), et leur asymptotique dans la limite des grandes tailles.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132081079","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}

{"title":"Non-resonant circles for strong magnetic fields on surfaces","authors":"L. Asselle, G. Benedetti","doi":"10.5802/ahl.147","DOIUrl":"https://doi.org/10.5802/ahl.147","url":null,"abstract":"We study non-resonant circles for strong magnetic fields on a closed, connected, oriented surface and show how these can be used to prove the existence of trapping regions and of periodic magnetic geodesics with prescribed low speed. As a corollary, there exist infinitely many periodic magnetic geodesics for every low speed in the following cases: i) the surface is not the two-sphere, ii) the magnetic field vanishes somewhere.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123886744","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}

{"title":"Probabilistic construction of Toda Conformal Field Theories","authors":"Baptiste Cercl'e, Rémi Rhodes, V. Vargas","doi":"10.5802/ahl.158","DOIUrl":"https://doi.org/10.5802/ahl.158","url":null,"abstract":"Following the 1984 seminal work of Belavin, Polyakov and Zamolodchikov on two-dimensional conformal field theories, Toda conformal field theories were introduced in the physics literature as a family of two-dimensional conformal field theories that enjoy, in addition to conformal symmetry, an extended level of symmetry usually referred to as W-symmetry or higher-spin symmetry. More precisely Toda conformal field theories provide a natural way to associate to a finite-dimensional simple and complex Lie algebra a conformal field theory for which the algebra of symmetry contains the Virasoro algebra. In this document we use the path integral formulation of these models to provide a rigorous mathematical construction of Toda conformal field theories based on probability theory. By doing so we recover expected properties of the theory such as the Weyl anomaly formula with respect to the change of background metric by a conformal factor and the existence of Seiberg bounds for the correlation functions.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125547248","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}

{"title":"Probabilistic enumerative geometry over p-adic numbers: linear spaces on complete intersections","authors":"Rida Ait El Manssour, A. Lerário","doi":"10.5802/ahl.153","DOIUrl":"https://doi.org/10.5802/ahl.153","url":null,"abstract":"We compute the expectation of the number of linear spaces on a random complete intersection in $p$-adic projective space. Here \"random\" means that the coefficients of the polynomials defining the complete intersections are sampled uniformly form the $p$-adic integers. We show that as the prime $p$ tends to infinity the expected number of linear spaces on a random complete intersection tends to $1$. In the case of the number of lines on a random cubic in three-space and on the intersection of two random quadrics in four-space, we give an explicit formula for this expectation.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126177887","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}