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Rational maps with rational multipliers 具有有理乘数的有理映射
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-10-31 DOI: 10.5802/jep.227
Valentin Huguin
{"title":"Rational maps with rational multipliers","authors":"Valentin Huguin","doi":"10.5802/jep.227","DOIUrl":"https://doi.org/10.5802/jep.227","url":null,"abstract":"In this article, we show that every rational map whose multipliers all lie in a given number field is a power map, a Chebyshev map or a Latt`{e}s map. This strengthens a conjecture by Milnor concerning rational maps with integer multipliers, which was recently proved by Ji and Xie.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"303 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131420739","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
Global pluripotential theory on hybrid spaces 混合空间的全局多势理论
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-09-11 DOI: 10.5802/jep.228
L'eonard Pille-Schneider
{"title":"Global pluripotential theory on hybrid spaces","authors":"L'eonard Pille-Schneider","doi":"10.5802/jep.228","DOIUrl":"https://doi.org/10.5802/jep.228","url":null,"abstract":"Let A be an integral Banach ring, and X/A be a projective scheme of finite type, endowed with a semi-ample line bundle L. We define a class PSH(X,L) of plurisubharmonic metrics on L on the Berkovich analytification X^an and prove various basic properties thereof. We focus in particular on the case where A is a hybrid ring of complex power series and X/A is a smooth variety, so that X^an is the hybrid space associated to a degeneration X of complex varieties over the punctured disk. We then prove that when L is ample, any plurisubharmonic metric on L with logarithmic growth at zero admits a canonical plurisubharmonic extension to the hybrid space X^hyb . We also discuss the continuity of the family of Monge-Amp`ere measures associated to a continuous plurisubharmonic hybrid metric. In the case where X is a degeneration of canonically polarized manifolds, we prove that the canonical psh extension is continuous on Xhyb and describe it explicitly in terms of the canonical model (in the sense of MMP) of the degeneration.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127684574","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
Desensitizing control for the heat equation with respect to domain variations 与域变化有关的热方程脱敏控制
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-09-08 DOI: 10.5802/jep.209
S. Ervedoza, P. Lissy, Y. Privat
{"title":"Desensitizing control for the heat equation with respect to domain variations","authors":"S. Ervedoza, P. Lissy, Y. Privat","doi":"10.5802/jep.209","DOIUrl":"https://doi.org/10.5802/jep.209","url":null,"abstract":". — This article is dedicated to desensitizing issues for a quadratic functional involving the solution of the linear heat equation with respect to domain variations. This work can be seen as a continuation of [28], insofar as we generalize several of the results it contains and investigate new related properties. In our framework, we consider variations of the spatial domain on which the solution of the PDE is defined at each time, and investigate three main issues: (i) approximate desensitizing, (ii) approximate desensitizing combined with an exact desensitizing for a finite-dimensional subspace, and (iii) exact desensitizing. We provide positive answers to questions (i) and (ii) and partial results to question (iii). pour","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126241266","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
Erratum to “Completed Iwahori-Hecke algebra and parahoric Hecke algebras for Kac-Moody groups over local fields” “局部域上Kac-Moody群的完整Iwahori-Hecke代数和拟Hecke代数”的勘误
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-08-25 DOI: 10.5802/jep.206
Ramla Abdellatif, Auguste Hébert
{"title":"Erratum to “Completed Iwahori-Hecke algebra and parahoric Hecke algebras for Kac-Moody groups over local fields”","authors":"Ramla Abdellatif, Auguste Hébert","doi":"10.5802/jep.206","DOIUrl":"https://doi.org/10.5802/jep.206","url":null,"abstract":". — We modify the definition of the completed Iwahori-Hecke algebra given in our previous article (J. Éc. Polytechnique 6 , and explain why the construction we gave earlier is not correct as such.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117149301","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
The noncommutative factor theorem for lattices in product groups 乘积群中格的非交换因子定理
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-07-27 DOI: 10.5802/jep.223
R. Boutonnet, Cyril Houdayer
{"title":"The noncommutative factor theorem for lattices in product groups","authors":"R. Boutonnet, Cyril Houdayer","doi":"10.5802/jep.223","DOIUrl":"https://doi.org/10.5802/jep.223","url":null,"abstract":"We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible lattices $Gamma<G$ in higher rank semisimple algebraic groups. Namely, we give a complete description of all intermediate von Neumann subalgebras $operatorname{L}(Gamma) subset M subset operatorname{L}(Gamma curvearrowright G/P)$ sitting between the group von Neumann algebra and the group measure space von Neumann algebra associated with the action on the Furstenberg-Poisson boundary.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121259251","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
Effective operators on an attractive magnetic edge 有吸引力的磁边上的有效算子
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-07-27 DOI: 10.5802/jep.236
S. Fournais, B. Helffer, Ayman Kachmar, N. Raymond
{"title":"Effective operators on an attractive magnetic edge","authors":"S. Fournais, B. Helffer, Ayman Kachmar, N. Raymond","doi":"10.5802/jep.236","DOIUrl":"https://doi.org/10.5802/jep.236","url":null,"abstract":"The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an attractive magnetic edge. Various accurate spectral asymptotics are established by means of a dimensional reduction involving a microlocal phase space localization allowing to deal with the discontinuity of the field.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126258928","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: 3
A characterisation of the continuum Gaussian free field in arbitrary dimensions 任意维连续高斯自由场的表征
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-06-30 DOI: 10.5802/jep.201
Juhan Aru, E. Powell
{"title":"A characterisation of the continuum Gaussian free field in arbitrary dimensions","authors":"Juhan Aru, E. Powell","doi":"10.5802/jep.201","DOIUrl":"https://doi.org/10.5802/jep.201","url":null,"abstract":". — We prove that under certain mild moment and continuity assumptions, the d -dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition of the underlying functional space in terms of radial processes and spherical harmonics. Résumé (Une caractérisation du champ libre gaussien dans le continu en toute dimension) Nous montrons que, sous de faibles hypothèses de moment et de continuité, le champ libre gaussien dans le continu à d dimensions est le seul processus stochastique satisfaisant à la propriété habituelle de Markov sur le domaine et une propriété d’échelle. Notre preuve est basée sur une décomposition de l’espace fonctionnel sous-jacent en termes de processus radiaux et d’harmoniques sphériques.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126633936","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
Mixing time and expansion of non-negatively curved Markov chains 非负弯曲马尔可夫链的混合时间与展开
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-06-16 DOI: 10.5802/jep.226
Florentin Münch, J. Salez
{"title":"Mixing time and expansion of non-negatively curved Markov chains","authors":"Florentin Münch, J. Salez","doi":"10.5802/jep.226","DOIUrl":"https://doi.org/10.5802/jep.226","url":null,"abstract":"We establish three remarkable consequences of non-negative curvature for sparse Markov chains. First, their conductance decreases logarithmically with the number of states. Second, their displacement is at least diffusive until the mixing time. Third, they never exhibit the cutoff phenomenon. The first result provides a nearly sharp quantitative answer to a classical question of Ollivier, Milman and Naor. The second settles a conjecture of Lee and Peres for graphs with non-negative curvature. The third offers a striking counterpoint to the recently established cutoff for non-negatively curved chains with uniform expansion.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132401653","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
The diagonal of the multiplihedra and the tensor product of A ∞ -morphisms 复面体的对角线和A∞-态射的张量积
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-06-11 DOI: 10.5802/jep.221
Guillaume Laplante-Anfossi, Thibaut Mazuir
{"title":"The diagonal of the multiplihedra and the tensor product of A ∞ -morphisms","authors":"Guillaume Laplante-Anfossi, Thibaut Mazuir","doi":"10.5802/jep.221","DOIUrl":"https://doi.org/10.5802/jep.221","url":null,"abstract":"We define a cellular approximation for the diagonal of the Forcey--Loday realizations of the multiplihedra, and endow them with a compatible topological cellular operadic bimodule structure over the Loday realizations of the associahedra. This provides us with a model for topological and algebraic A-infinity morphisms, as well as a universal and explicit formula for their tensor product. We study the monoidal properties of this newly defined tensor product and conclude by outlining several applications, notably in algebraic and symplectic topology.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127480474","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
On systems of particles in singular repulsive interaction in dimension one: log and Riesz gas 一维奇异排斥相互作用中的粒子系统:对数和Riesz气体
Journal de l’École polytechnique — Mathématiques Pub Date : 2022-04-22 DOI: 10.5802/jep.235
A. Guillin, Pierre Le Bris, Pierre Monmarch'e
{"title":"On systems of particles in singular repulsive interaction in dimension one: log and Riesz gas","authors":"A. Guillin, Pierre Le Bris, Pierre Monmarch'e","doi":"10.5802/jep.235","DOIUrl":"https://doi.org/10.5802/jep.235","url":null,"abstract":"In this article, we prove the first quantitative uniform in time propagation of chaos for a class of systems of particles in singular repulsive interaction in dimension one that contains the Dyson Brownian motion. We start by establishing existence and uniqueness for the Riesz gases, before proving propagation of chaos with an original approach to the problem, namely coupling with a Cauchy sequence type argument. We also give a general argument to turn a result of weak propagation of chaos into a strong and uniform in time result using the long time behavior and some bounds on moments, in particular enabling us to get a uniform in time version of the result of C'epa-L'epingle.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123458812","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: 3
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