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Formules de Feynmann-Kac pour le modèle de Nelson ultra-violet renormalisée 重整化Nelson紫外模型的Feynmann-Kac公式
IF 1.1 4区 数学
Asterisque Pub Date : 2017-01-10 DOI: 10.24033/ast.1054
O. Matte, J. S. Møller
{"title":"Formules de Feynmann-Kac pour le modèle de Nelson ultra-violet renormalisée","authors":"O. Matte, J. S. Møller","doi":"10.24033/ast.1054","DOIUrl":"https://doi.org/10.24033/ast.1054","url":null,"abstract":"We derive Feynman-Kac formulas for the ultra-violet renormalized Nelson Hamiltonian with a Kato decomposable external potential and for corresponding fiber Hamiltonians in the translation invariant case. We simultaneously treat massive and massless bosons. Furthermore, we present a non-perturbative construction of a renormalized Nelson Hamiltonian in the non-Fock representation defined as the generator of a corresponding Feynman-Kac semi-group. Our novel analysis of the vacuum expectation of the Feynman-Kac integrands shows that, if the external potential and the Pauli-principle are dropped, then the spectrum of the $N$-particle renormalized Nelson Hamiltonian is bounded from below by some negative universal constant times $g^4N^3$, for all values of the coupling constant $g$. A variational argument also yields an upper bound of the same form for large $g^2N$. We further verify that the semi-groups generated by the ultra-violet renormalized Nelson Hamiltonian and its non-Fock version are positivity improving with respect to a natural self-dual cone, if the Pauli principle is ignored. In another application we discuss continuity properties of elements in the range of the semi-group of the renormalized Nelson Hamiltonian.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2017-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49027673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
A C^1 Arnol'd-Liouville theorem C^1阿诺-刘维尔定理
IF 1.1 4区 数学
Asterisque Pub Date : 2016-12-23 DOI: 10.24033/ast.1109
M. Arnaud, Jinxin Xue
{"title":"A C^1 Arnol'd-Liouville theorem","authors":"M. Arnaud, Jinxin Xue","doi":"10.24033/ast.1109","DOIUrl":"https://doi.org/10.24033/ast.1109","url":null,"abstract":"In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial to determine the Dynamics on each Lagrangian torus and that the C 1 regularity of the foliation by invariant Lagrangian tori is crucial to prove the continuity of Arnol'd-Liouville coordinates. We also explore various notions of C 0 and Lipschitz integrability.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68829818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Tilting modules and the p-canonical basis 倾斜模与p-正则基
IF 1.1 4区 数学
Asterisque Pub Date : 2015-12-28 DOI: 10.24033/ast.1041
S. Riche, G. Williamson
{"title":"Tilting modules and the p-canonical basis","authors":"S. Riche, G. Williamson","doi":"10.24033/ast.1041","DOIUrl":"https://doi.org/10.24033/ast.1041","url":null,"abstract":"In this paper we propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. We conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on the principal block. Our conjecture implies character formulas for the simple and tilting modules in terms of the p-canonical basis, as well as a description of the principal block as the anti-spherical quotient of the Hecke category. We prove our conjecture for GL_n using the theory of 2-Kac-Moody actions. Finally, we prove that the diagrammatic Hecke category of a general crystallographic Coxeter group may be described in terms of parity complexes on the flag variety of the corresponding Kac-Moody group.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2015-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68827540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 131
AST418 - A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case 酉群的Gan-Gross-Prasad猜想的一个局部迹公式:阿基米德情况
IF 1.1 4区 数学
Asterisque Pub Date : 2015-06-04 DOI: 10.24033/ast.1120
Raphael Beuzart-Plessis
{"title":"AST418 - A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case","authors":"Raphael Beuzart-Plessis","doi":"10.24033/ast.1120","DOIUrl":"https://doi.org/10.24033/ast.1120","url":null,"abstract":"In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic zero. As a consequence, we obtain a geometric formula for certain multiplicities $m(pi)$ appearing in this conjecture and deduce from it a weak form of the local Gan-Gross-Prasad conjecture (multiplicity one in tempered L-packets). These results were already known over $p$-adic fields and thus are only new when $F=mathbb{R}$.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2015-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68830507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
The Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane 仿射平面多项式自同态的动力学模型-朗猜想
IF 1.1 4区 数学
Asterisque Pub Date : 2015-03-02 DOI: 10.24033/ast.1038
Junyi Xie
{"title":"The Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane","authors":"Junyi Xie","doi":"10.24033/ast.1038","DOIUrl":"https://doi.org/10.24033/ast.1038","url":null,"abstract":"In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2015-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68827452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
Periods and harmonic analysis on spherical varieties 球形品种的周期和谐波分析
IF 1.1 4区 数学
Asterisque Pub Date : 2012-02-29 DOI: 10.24033/ast.1040
Y. Sakellaridis, Akshay Venkatesh
{"title":"Periods and harmonic analysis on spherical varieties","authors":"Y. Sakellaridis, Akshay Venkatesh","doi":"10.24033/ast.1040","DOIUrl":"https://doi.org/10.24033/ast.1040","url":null,"abstract":"Given a spherical variety X for a group G over a non-archimedean local field k, the Plancherel decomposition for L^2(X) should be related to \"distinguished\" Arthur parameters into a dual group closely related to that defined by Gaitsgory and Nadler. Motivated by this, we develop, under some assumptions on the spherical variety, a Plancherel formula for L^2(X) up to discrete (modulo center) spectra of its \"boundary degenerations\", certain G-varieties with more symmetries which model X at infinity. Along the way, we discuss the asymptotic theory of subrepresentations of C^{infty}(X), and establish conjectures of Ichino-Ikeda and Lapid-Mao. We finally discuss global analogues of our local conjectures, concerning the period integrals of automorphic forms over spherical subgroups.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2012-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68827473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 194
Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions] 粗糙系数常微分方程与Ambrosio的重整化定理[源自Ambrosio, DiPerna, Lions]
IF 1.1 4区 数学
Asterisque Pub Date : 2008-01-01 DOI: 10.5167/UZH-21441
Camillo De Lellis
{"title":"Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions]","authors":"Camillo De Lellis","doi":"10.5167/UZH-21441","DOIUrl":"https://doi.org/10.5167/UZH-21441","url":null,"abstract":"In a seminal paper of almost 20 years ago, R.J. DiPerna and P.-L. Lions initiated the theory of renormalized solutions to study the well-posedness of Ordinary Differential Equations and Transport Equations with discontinuous coefficients. In a recent work L. Ambrosio solved the long-standing open problem of extending this theory to BV coefficients, the most common functional-analytic closure of classical functions with jump discontinuities. Besides its intrinsic interest, Ambrosio's Theorem has been used to solve relevant problems in Partial Differential Equations and it opened the way to a series of new questions.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70645995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
H[∞]functional calculus and square functions on noncommutative L[p]-spaces 非交换L[p]-空间上的H[∞]泛函微积分与平方函数
IF 1.1 4区 数学
Asterisque Pub Date : 2006-12-01 DOI: 10.24033/AST.698
M. Junge, C. Merdy, Quanhua Xu
{"title":"H[∞]functional calculus and square functions on noncommutative L[p]-spaces","authors":"M. Junge, C. Merdy, Quanhua Xu","doi":"10.24033/AST.698","DOIUrl":"https://doi.org/10.24033/AST.698","url":null,"abstract":"— We investigate sectorial operators and semigroups acting on noncommutative L-spaces. We introduce new square functions in this context and study their connection with H∞ functional calculus, extending some famous work by Cowling, Doust, McIntoch and Yagi concerning commutative L-spaces. This requires natural variants of Rademacher sectoriality and the use of the matricial structure of noncommutative L-spaces. We mainly focus on noncommutative diffusion semigroups, that is, semigroups (Tt)t≥0 of normal selfadjoint operators on a semifinite von Neumann algebra (M, τ) such that Tt : Lp(M) → Lp(M) is a contraction for any p ≥ 1 and any t ≥ 0. We discuss several examples of such semigroups for which we establish bounded H∞ functional calculus and square function estimates. This includes semigroups generated by certain Hamiltonians or Schur multipliers, q-Ornstein-Uhlenbeck semigroups acting on the q-deformed von Neumann algebras of Bozejko-Speicher, and the noncommutative Poisson semigroup acting on the group von Neumann algebra of a free group. c © Astérisque 305, SMF 2006","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68830844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 94
Quantum integrable systems 量子可积系统
IF 1.1 4区 数学
Asterisque Pub Date : 1994-01-01 DOI: 10.1090/cbms/125/11
M. Semenov-Tian-Shansky
{"title":"Quantum integrable systems","authors":"M. Semenov-Tian-Shansky","doi":"10.1090/cbms/125/11","DOIUrl":"https://doi.org/10.1090/cbms/125/11","url":null,"abstract":"© Société mathématique de France, 1995, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"1994-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60549305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Minimal K-types for GLn over a p-adic field p进域上GLn的最小k型
IF 1.1 4区 数学
Asterisque Pub Date : 1988-01-01 DOI: 10.2307/2000877
R. Howe, A. Moy
{"title":"Minimal K-types for GLn over a p-adic field","authors":"R. Howe, A. Moy","doi":"10.2307/2000877","DOIUrl":"https://doi.org/10.2307/2000877","url":null,"abstract":"© Société mathématique de France, 1989, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2307/2000877","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68734049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 21
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