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Annales Henri Lebesgue最新文献

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On the algebraic dependence of holonomic functions 关于完整函数的代数相关性
Annales Henri Lebesgue Pub Date : 2020-11-03 DOI: 10.5802/ahl.120
J. Roques, M. Singer
{"title":"On the algebraic dependence of holonomic functions","authors":"J. Roques, M. Singer","doi":"10.5802/ahl.120","DOIUrl":"https://doi.org/10.5802/ahl.120","url":null,"abstract":"We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and are algebraically dependent, we give conditions on the differential Galois group associated to f guaranteeing that g is a polynomial in f. We apply this to hypergeometric functions and iterated integrals.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"36 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116616753","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
Yaglom-type limit theorems for branching Brownian motion with absorption 带吸收的分支布朗运动的yaglom型极限定理
Annales Henri Lebesgue Pub Date : 2020-10-30 DOI: 10.5802/ahl.140
Pascal Maillard, Jason Schweinsberg
{"title":"Yaglom-type limit theorems for branching Brownian motion with absorption","authors":"Pascal Maillard, Jason Schweinsberg","doi":"10.5802/ahl.140","DOIUrl":"https://doi.org/10.5802/ahl.140","url":null,"abstract":"We consider one-dimensional branching Brownian motion in which particles are absorbed at the origin. We assume that when a particle branches, the offspring distribution is supercritical, but the particles are given a critical drift towards the origin so that the process eventually goes extinct with probability one. We establish precise asymptotics for the probability that the process survives for a large time t, building on previous results by Kesten (1978) and Berestycki, Berestycki, and Schweinsberg (2014). We also prove a Yaglom-type limit theorem for the behavior of the process conditioned to survive for an unusually long time, providing an essentially complete answer to a question first addressed by Kesten (1978). An important tool in the proofs of these results is the convergence of a certain observable to a continuous state branching process. Our proofs incorporate new ideas which might be of use in other branching models.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126654812","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: 12
Cayley graphs with few automorphisms: the case of infinite groups 少自同构的Cayley图:无限群的情况
Annales Henri Lebesgue Pub Date : 2020-10-12 DOI: 10.5802/ahl.118
P. Leemann, M. Salle
{"title":"Cayley graphs with few automorphisms: the case of infinite groups","authors":"P. Leemann, M. Salle","doi":"10.5802/ahl.118","DOIUrl":"https://doi.org/10.5802/ahl.118","url":null,"abstract":"We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every finitely generated group admits a Cayley graph with countable automorphism group. We also treat the case of directed graphs.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128114502","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
A block moment method to handle spectral condensation phenomenon in parabolic control problems 处理抛物控制问题中频谱凝聚现象的块矩法
Annales Henri Lebesgue Pub Date : 2020-08-24 DOI: 10.5802/AHL.45
A. Benabdallah, Franck Boyer, Morgan Morancey
{"title":"A block moment method to handle spectral condensation phenomenon in parabolic control problems","authors":"A. Benabdallah, Franck Boyer, Morgan Morancey","doi":"10.5802/AHL.45","DOIUrl":"https://doi.org/10.5802/AHL.45","url":null,"abstract":"This article is devoted to the characterization of the minimal null control time for abstract linear controlled problem. More precisely we aim at giving a precise answer to the following question: what is the minimal time needed to drive the solution of the system starting from any initial condition in a given subspace to zero ? Our setting will encompass a wide variety of systems of coupled one dimensional linear parabolic equations with a scalar control. Following classical ideas we reduce this controllability issue to the resolution of a moment problem on the control and provide a new block resolution technique for this moment problem. The obtained estimates are sharp and hold uniformly for a certain class of operators. This uniformity will allow various applications for parameter dependant control problems and permitted us to deal naturally with the case of algebraically multiple eigenvalues in the underlying generator. Our approach shed light on a new phenomenon: the condensation of eigenvalues (which can cause a non zero minimal null control time in general) can be somehow compensated by the condensation of eigenvectors. We provide various examples (some are abstract systems, others are actual PDE systems) to highlight those new situations we are able to manage by the block resolution of the moment problem we propose.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131191542","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: 2
Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems 二重(拟)泊松代数的态射与可积系统的作用角对偶
Annales Henri Lebesgue Pub Date : 2020-08-04 DOI: 10.5802/ahl.121
M. Fairon
{"title":"Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems","authors":"M. Fairon","doi":"10.5802/ahl.121","DOIUrl":"https://doi.org/10.5802/ahl.121","url":null,"abstract":"Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of algebras endowed with a (quasi-)Poisson bracket. In this work, we provide a study of morphisms of double (quasi-)Poisson algebras, which we relate to the $H_0$-Poisson structures of Crawley-Boevey. We derive from our results a representation theoretic description of action-angle duality for several classical integrable systems.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131961181","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
Proof of the strong Scott conjecture for heavy atoms: the Furry picture 重原子强斯科特猜想的证明:弗里斯图
Annales Henri Lebesgue Pub Date : 2020-07-08 DOI: 10.5802/ahl.131
Konstantin Merz, H. Siedentop
{"title":"Proof of the strong Scott conjecture for heavy atoms: the Furry picture","authors":"Konstantin Merz, H. Siedentop","doi":"10.5802/ahl.131","DOIUrl":"https://doi.org/10.5802/ahl.131","url":null,"abstract":"We prove the convergence of the density on the scale $Z^{-1}$ to the density of the Bohr atom (with infinitely many electrons) (strong Scott conjecture) for a model that is known to describe heavy atoms accurately.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128342178","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: 2
Stability of steady states for Hartree and Schrödinger equations for infinitely many particles 无穷多粒子的Hartree方程和Schrödinger方程的稳态稳定性
Annales Henri Lebesgue Pub Date : 2020-07-01 DOI: 10.5802/ahl.127
Charles Collot, A. Suzzoni
{"title":"Stability of steady states for Hartree and Schrödinger equations for infinitely many particles","authors":"Charles Collot, A. Suzzoni","doi":"10.5802/ahl.127","DOIUrl":"https://doi.org/10.5802/ahl.127","url":null,"abstract":"We prove a scattering result for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation for density matrices. We treat dimensions 2 and 3, extending our previous result [11]. We reach a large class of interaction potentials, which includes the nonlinear Schrodinger equation. This result has an incidence in the density matrices framework. The proof relies on dispersive techniques used for the study of scattering for the nonlinear Schrodinger equation , and on the use of explicit low frequency cancellations as in [24]. To relate to density matrices, we use Strichartz estimates for orthonormal systems from [16], and improved Leibniz rules for integral operators.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131059013","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
Gradient flow approach to the calculation of stationary states on nonlinear quantum graphs 梯度流法在非线性量子图上的稳态计算
Annales Henri Lebesgue Pub Date : 2020-06-08 DOI: 10.5802/ahl.126
C. Besse, Romain Duboscq, Stefan Le Coz
{"title":"Gradient flow approach to the calculation of stationary states on nonlinear quantum graphs","authors":"C. Besse, Romain Duboscq, Stefan Le Coz","doi":"10.5802/ahl.126","DOIUrl":"https://doi.org/10.5802/ahl.126","url":null,"abstract":"We introduce and implement a method to compute stationary states of nonlinear Schr''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the nonlinear Schr''odinger energy at fixed mass. Our method is based on a normalized gradient flow for the energy (i.e. a gradient flow projected on a fixed mass sphere) adapted to the context of nonlinear quantum graphs. We first prove that, at the continuous level, the normalized gradient flow is well-posed, mass-preserving, energy diminishing and converges (at least locally) towards stationary states. We then establish the link between the continuous flow and its discretized version. We conclude by conducting a series of numerical experiments in model situations showing the good performance of the discrete flow to compute stationary states. Further experiments as well as detailed explanation of our numerical algorithm are given in a companion paper.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115538594","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
The effect of discretization on the mean geometry of a 2D random field 离散化对二维随机场平均几何形状的影响
Annales Henri Lebesgue Pub Date : 2020-06-05 DOI: 10.5802/ahl.103
H. Biermé, A. Desolneux
{"title":"The effect of discretization on the mean geometry of a 2D random field","authors":"H. Biermé, A. Desolneux","doi":"10.5802/ahl.103","DOIUrl":"https://doi.org/10.5802/ahl.103","url":null,"abstract":"The study of the geometry of excursion sets of 2D random fields is a question of interest from both the theoretical and the applied viewpoints. In this paper we are interested in the relationship between the perimeter (resp. the total curvature, related to the Euler characteristic by Gauss-Bonnet Theorem) of the excursion sets of a function and the ones of its discretization. Our approach is a weak framework in which we consider the functions that map the level of the excursion set to the perimeter (resp. the total curvature) of the excursion set. We will be also interested in a stochastic framework in which the sets are the excursion sets of 2D random fields. We show in particular that, in expectation, under some stationarity and isotropy conditions on the random field, the perimeter is always biased (with a 4/π factor), whereas the total curvature is not. We illustrate all our results on different examples of random fields.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127862160","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
Variations in the distribution of principally polarized abelian varieties among isogeny classes 主极化阿贝尔变异在同系类间分布的变化
Annales Henri Lebesgue Pub Date : 2020-05-29 DOI: 10.5802/ahl.133
Everett W. Howe
{"title":"Variations in the distribution of principally polarized abelian varieties among isogeny classes","authors":"Everett W. Howe","doi":"10.5802/ahl.133","DOIUrl":"https://doi.org/10.5802/ahl.133","url":null,"abstract":"We show that for a large class of rings $R$, the number of principally polarized abelian varieties over a finite field in a given simple ordinary isogeny class and with endomorphism ring $R$ is equal either to 0, or to a ratio of class numbers associated to $R$, up to some small computable factors. This class of rings includes the maximal order of the CM field $K$ associated to the isogeny class (for which the result was already known), as well as the order $R$ generated over $mathbf{Z}$ by Frobenius and Verschiebung. \u0000For this latter order, we can use results of Louboutin to estimate the appropriate ratio of class numbers in terms of the size of the base field and the Frobenius angles of the isogeny class. The error terms in our estimates are quite large, but the trigonometric terms in the estimate are suggestive: Combined with a result of Vladut on the distribution of Frobenius angles of isogeny classes, they give a heuristic argument in support of the theorem of Katz and Sarnak on the limiting distribution of the multiset of Frobenius angles for principally polarized abelian varieties of a fixed dimension over finite fields.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124321686","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
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