Journal de l’École polytechnique — Mathématiques最新文献_第9页

Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions 二阶线性差分方程和椭圆型超几何函数的微分超越准则

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-09-22 DOI: 10.5802/JEP.143

Carlos E. Arreche, T. Dreyfus, J. Roques

引用次数: 4

Maximal determinants of Schrödinger operators on bounded intervals 有界区间上Schrödinger算子的极大行列式

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-09-12 DOI: 10.5802/jep.128

C. Aldana, Jean-Baptiste Caillau, P. Freitas

引用次数: 0

Hölder regularity for the spectrum of translation flows Hölder翻译流谱的规律性

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-08-25 DOI: 10.5802/JEP.146

A. Bufetov, B. Solomyak

引用次数: 11

Null-controllability of linear parabolic-transport systems 线性抛物输运系统的无可控性

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-07-22 DOI: 10.5802/jep.127

K. Beauchard, Armand Koenig, K. L. Balc'h

{"title":"Null-controllability of linear parabolic-transport systems","authors":"K. Beauchard, Armand Koenig, K. L. Balc'h","doi":"10.5802/jep.127","DOIUrl":"https://doi.org/10.5802/jep.127","url":null,"abstract":"Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find a unified framework that encompasses and generalizes the previous results. \u0000We consider constant coefficients heat-transport systems with coupling of order zero and one, with a locally distributed control in the source term, posed on the one dimensional torus. \u0000We prove the null-controllability, in optimal time (the one expected because of the transport component) when there is as much controls as equations. When the control acts only on the transport (resp. parabolic) component, we prove an algebraic necessary and sufficient condition, on the coupling term, for the null controllability. \u0000The whole study relies on a careful spectral analysis, based on perturbation theory. The negative controllability result in small time is proved on solutions localized on high hyperbolic frequencies, that solve a pure transport equation up to a compact term. The proof of the positive result in large time relies on a spectral decomposition into low, and asymptotically parabolic or hyperbolic frequencies.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"356 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133725225","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

Quotients of groups of birational transformations of cubic del Pezzo fibrations 三次del Pezzo颤振的两族变换群商

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-07-10 DOI: 10.5802/jep.136

J. Blanc, E. Yasinsky

引用次数: 13

Positive harmonic functions on the Heisenberg group II 海森堡群II上的正调和函数

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-07-09 DOI: 10.5802/JEP.163

Y. Benoist

引用次数: 2

Quasi-stationary distributions and resilience: what to get from a sample? 准平稳分布和弹性:从样本中得到什么?

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-06-13 DOI: 10.5802/jep.132

J. Chazottes, P. Collet, S. Martínez, S. Méléard

{"title":"Quasi-stationary distributions and resilience: what to get from a sample?","authors":"J. Chazottes, P. Collet, S. Martínez, S. Méléard","doi":"10.5802/jep.132","DOIUrl":"https://doi.org/10.5802/jep.132","url":null,"abstract":"We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by $K$ and in the limit $Kto+infty$, the realizations of such processes get close, in any fixed finite-time window, to the trajectories of a dynamical system whose vector field is defined by the birth and death rates. Assuming that this dynamical has a unique attracting fixed point, we analyzed in a previous work what happens for large but finite $K$, especially the different time scales showing up. In the present work, we are mainly interested in the following question: Observing a realization of the process, can we determine the so-called engineering resilience? To answer this question, we establish two relations which intermingle the resilience, which is a macroscopic quantity defined for the dynamical system, and the fluctuations of the process, which are microscopic quantities. Analogous relations are well known in nonequilibrium statistical mechanics. To exploit these relations, we need to introduce several estimators which we control for times between $log K$ (time scale to converge to the qsd) and $exp(K)$ (time scale of mean time to extinction).","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123751829","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

Homogenization of linear transport equations. A new approach 线性输运方程的均匀化。新方法

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-05-22 DOI: 10.5802/jep.122

M. Briane

引用次数: 4

On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity 非局部遍历Jacobi半群:谱理论、收敛至平衡和收缩性

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-05-20 DOI: 10.5802/JEP.148

Patrick Cheridito, P. Patie, A. Srapionyan, A. Vaidyanathan

{"title":"On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity","authors":"Patrick Cheridito, P. Patie, A. Srapionyan, A. Vaidyanathan","doi":"10.5802/JEP.148","DOIUrl":"https://doi.org/10.5802/JEP.148","url":null,"abstract":"In this paper, we introduce and study non-local Jacobi operators, which generalize the classical (local) Jacobi operator. We show that these operators extend to the generator of an ergodic Markov semigroup with a unique invariant probability measure and study its spectral and convergence properties. In particular, we give a series expansion of the semigroup in terms of explicitly defined polynomials, which are counterparts of the classical Jacobi orthogonal polynomials. In addition, we give a complete characterization of the spectrum of the non-self-adjoint generator and semigroup. We show that the variance decay of the semigroup is hypocoercive with explicit constants, which provides a natural generalization of the spectral gap estimate. After a random warm-up time, the semigroup also decays exponentially in entropy and is both hypercontractive and ultracontractive. Our proofs hinge on the development of commutation identities, known as intertwining relations, between local and non-local Jacobi operators/semigroups, with the local Jacobi operator/semigroup serving as a reference object for transferring properties to the non-local ones.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134379366","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

Pink’s conjecture on unlikely intersections and families of semi-abelian varieties 平克关于不可能交集和半阿贝尔变种族的猜想

Journal de l’École polytechnique — Mathématiques Pub Date : 2019-04-03 DOI: 10.5802/jep.126

D. Bertrand, B. Edixhoven

引用次数: 6