Annales Henri Lebesgue最新文献

{"title":"On a stochastic Hardy–Littlewood–Sobolev inequality with application to Strichartz estimates for a noisy dispersion","authors":"Romain Duboscq, Anthony Reveillac","doi":"10.5802/ahl.122","DOIUrl":"https://doi.org/10.5802/ahl.122","url":null,"abstract":"In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the non-homogenous nature of the potential in the inequality, a constant proportional to the length of the interval appears on the right-hand-side. As a direct application, we derive local Strichartz estimates for randomly modulated dispersions and solve the Cauchy problem of the critical nonlinear Schrödinger equation.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123220956","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":"An effective weighted K-stability condition for polytopes and semisimple principal toric fibrations","authors":"Thibaut Delcroix, S. Jubert","doi":"10.5802/ahl.161","DOIUrl":"https://doi.org/10.5802/ahl.161","url":null,"abstract":"The second author has shown that existence of extremal K\"ahler metrics on semisimple principal toric fibrations is equivalent to a notion of weighted uniform K-stability, read off from the moment polytope. The purpose of this article is to prove various sufficient conditions of weighted uniform K-stability which can be checked effectively and explore the low dimensional new examples of extremal K\"ahler metrics it provides.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121850533","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":"Decompletion of cyclotomic perfectoid fields in positive characteristic","authors":"L. Berger, S. Rozensztajn","doi":"10.5802/ahl.150","DOIUrl":"https://doi.org/10.5802/ahl.150","url":null,"abstract":"Let $E$ be a field of characteristic $p$. The group $mathbf{Z}_p^times$ acts on $E((X))$ by $a cdot f(X) = f((1+X)^a-1)$. This action extends to the $X$-adic completion $tilde{mathbf{E}}$ of $cup_{n geq 0} E((X^{1/p^n}))$. We show how to recover $E((X))$ from the valued $E$-vector space $tilde{mathbf{E}}$ endowed with its action of $mathbf{Z}_p^times$. To do this, we introduce the notion of super-H\"older vector in certain $E$-linear representations of $mathbf{Z}_p$. This is a characteristic $p$ analogue of the notion of locally analytic vector in $p$-adic Banach representations of $p$-adic Lie groups.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125517119","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":"Charmenability of higher rank arithmetic groups","authors":"U. Bader, R. Boutonnet, Cyril Houdayer","doi":"10.5802/ahl.166","DOIUrl":"https://doi.org/10.5802/ahl.166","url":null,"abstract":"We complete the study of characters on higher rank semisimple lattices initiated in [BH19,BBHP20], the missing case being the case of lattices in higher rank simple algebraic groups in arbitrary characteristics. More precisely, we investigate dynamical properties of the conjugation action of such lattices on their space of positive definite functions. Our main results deal with the existence and the classification of characters from which we derive applications to topological dynamics, ergodic theory, unitary representations and operator algebras. Our key theorem is an extension of the noncommutative Nevo-Zimmer structure theorem obtained in [BH19] to the case of simple algebraic groups defined over arbitrary local fields. We also deduce a noncommutative analogue of Margulis' factor theorem for von Neumann subalgebras of the noncommutative Poisson boundary of higher rank arithmetic groups.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123770612","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":"Multi-ended Markovian triangulations and robust convergence to the UIPT","authors":"Thomas Budzinski","doi":"10.5802/ahl.149","DOIUrl":"https://doi.org/10.5802/ahl.149","url":null,"abstract":"We classify completely the infinite, planar triangulations satisfying a weak spatial Markov property, without assuming one-endedness nor finiteness of vertex degrees. In particular, the Uniform Infinite Planar Triangulation (UIPT) is the only such triangulation with average degree 6. As a consequence, we prove that the convergence of uniform triangulations of the sphere to the UIPT is robust, in the sense that it is preserved under various perturbations of the uniform measure. As another application, we obtain large deviation estimates for the number of occurencies of a pattern in uniform triangulations.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114612913","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":"Approximate Schreier decorations and approximate Kőnig’s line coloring Theorem","authors":"Jan Grebík","doi":"10.5802/ahl.124","DOIUrl":"https://doi.org/10.5802/ahl.124","url":null,"abstract":"Following recent result of L. M. Tóth [arXiv:1906.03137] we show that every 2∆-regular Borel graph G with a (not necessarily invariant) Borel probability measure admits approximate Schreier decoration. In fact, we show that both ingredients from the analogous statements for finite graphs have approximate counterparts in the measurable setting, i.e., approximate König’s line coloring Theorem for Borel graphs without odd cycles and approximate balanced orientation for even degree Borel graphs. It is a standard fact from finite combinatorics that every 2∆-regular finite graph is a Schreier graph of the free group F∆ on ∆ generators. This means that every such graph admits an orientation and a ∆-labeling of the edges such that for every α ∈ ∆ and every vertex there is exactly one out-edge with label α and exactly one in-edge with label α. Such an orientation and labeling is called a Schreier decoration. Note that every Schreier decoration corresponds to an action of the free group F∆ on the vertex set of the graph. We refer the reader to the introduction in [11] for more information about Schreier decorations. The analogous statement for infinite graphs without any restriction on definability follows from the axiom of choice. In the measurable setting, i.e., when the vertex set is endowed with a standard probability (Borel) structure and we require the orientation and labeling to be measurable, the full analogue of the statement fails. This follows from the example of Laczkovich [9] who constructed an acyclic 2-regular bipartite graph on the unit interval that is not induced by an action of Z on any set of a full measure. However, Tóth recently proved [11] that if the measure is invariant one can always find a measurable Schreier decoration on a different graph that has the same local statistics. This can be stated in a compact form as follows: every 2∆-regular unimodular random rooted graph has an invariant random Schreier decoration, see [11, Theorem 1]. An equivalent formulation in a language that is closer to the one in this paper is as follows, see [11, Corollary 4]: Every 2∆-regular graphing (G, μ) is a local isomorphic copy of some graphing (G ′, μ′) that is induced by a Borel action of F∆ that preserves μ ′. The key steps in the proof of [11, Theorem 1] are (I) a consequence of [11, Theorem 3]: for every ∆-regular bipartite graphing (G, μ) and for every > 0 there is a Borel map c : E → ∆ that is a proper edge coloring on a set of μ-measure at least 1− , The author was supported by Leverhulme Research Project Grant RPG-2018-424.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126742593","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":"On the local times of noise reinforced Bessel processes","authors":"J. Bertoin","doi":"10.5802/ahl.151","DOIUrl":"https://doi.org/10.5802/ahl.151","url":null,"abstract":"We investigate the effects of noise reinforcement on a Bessel process of dimension $din(0,2)$, and more specifically on the asymptotic behavior of its additive functionals. This leads us to introduce a local time process and its inverse. We identify the latter as an increasing self-similar (time-homogeneous) Markov process, and from this, several explicit results can be deduced.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130634119","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":"Large deviations of convex hulls of planar random walks and Brownian motions","authors":"A. Akopyan, V. Vysotsky","doi":"10.5802/ahl.100","DOIUrl":"https://doi.org/10.5802/ahl.100","url":null,"abstract":". — We prove large deviations principles (LDPs) for the perimeter and the area of the convex hull of a planar random walk with finite Laplace transform of its increments. We give explicit upper and lower bounds for the rate function of the perimeter in terms of the rate function of the increments. These bounds coincide and thus give the rate function for pas optimaux en général.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130221518","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":"From invariant measures to orbit equivalence, via locally finite groups","authors":"Julien Melleray, Simon Robert","doi":"10.5802/ahl.165","DOIUrl":"https://doi.org/10.5802/ahl.165","url":null,"abstract":"We give a new proof of a theorem of Giordano, Putnam and Skau characterizing orbit equivalence of minimal homeomorphisms of the Cantor space in terms of their sets of invariant Borel probability measures. The proof is based on a strengtehning of a theorem of Krieger concerning minimal actions of certain locally finite groups of homeomorphisms, and we also give a new proof of the Giordano--Putnam--Skau characterization of orbit equivalence for these actions.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"36 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122691753","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":"Local-global principles for homogeneous spaces of reductive groups over global function fields","authors":"C. Demarche, David Harari","doi":"10.5802/ahl.144","DOIUrl":"https://doi.org/10.5802/ahl.144","url":null,"abstract":"Let $K$ be a global field of positive characteristic. We prove that the Brauer-Manin obstructions to the Hasse principle, to weak approximation and to strong approximation are the only ones for homogeneous spaces of reductive groups with reductive stabilizers. The methods involve abelianization techniques and arithmetic duality theorems for complexes of tori over K.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126002213","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}