J. Bruinier, Benjamin J. Howard, S. Kudla, M. Rapoport, Tonghai Yang, Keerthi Madapusi Pera
{"title":"Arithmetic divisors on orthogonal and unitary Shimura varieties","authors":"J. Bruinier, Benjamin J. Howard, S. Kudla, M. Rapoport, Tonghai Yang, Keerthi Madapusi Pera","doi":"10.24033/ast.1124","DOIUrl":"https://doi.org/10.24033/ast.1124","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"74 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68830578","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}
{"title":"Exposé Bourbaki 1163 : Manolescu's work on the Triangulation Conjecture","authors":"Andreas Stipsicz","doi":"10.24033/ast.1142","DOIUrl":"https://doi.org/10.24033/ast.1142","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68831321","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}
{"title":"Exposé Bourbaki 1162 : Transition de phase abrupte en percolation via des algorithmes randomisés (d'après Duminil-Copin, Raoufi et Tassion)","authors":"Marie Théret","doi":"10.24033/ast.1141","DOIUrl":"https://doi.org/10.24033/ast.1141","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68831311","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}
Let h(x) = {x} − 12 . We study the distribution of ∑n−1 k=0 h(x+ kα) when x is fixed, and n is sampled randomly uniformly in {1, . . . , N}, as N → ∞. Beck proved in [Bec10, Bec11] that if x = 0 and α is a quadratic irrational, then these distributions converge, after proper scaling, to the Gaussian distribution. We show that the set of α where a distributional scaling limit exists has Lebesgue measure zero, but that the following annealed limit theorem holds: Let (α, n) be chosen randomly uniformly in R/Z× {1, . . . , N}, then the distribution of ∑n−1 k=0 h(kα) converges after proper scaling as N →∞ to the Cauchy distribution.
{"title":"Quenched and annealed temporal limit theorems for circle rotations","authors":"D. Dolgopyat, O. Sarig","doi":"10.24033/ast.11100","DOIUrl":"https://doi.org/10.24033/ast.11100","url":null,"abstract":"Let h(x) = {x} − 12 . We study the distribution of ∑n−1 k=0 h(x+ kα) when x is fixed, and n is sampled randomly uniformly in {1, . . . , N}, as N → ∞. Beck proved in [Bec10, Bec11] that if x = 0 and α is a quadratic irrational, then these distributions converge, after proper scaling, to the Gaussian distribution. We show that the set of α where a distributional scaling limit exists has Lebesgue measure zero, but that the following annealed limit theorem holds: Let (α, n) be chosen randomly uniformly in R/Z× {1, . . . , N}, then the distribution of ∑n−1 k=0 h(kα) converges after proper scaling as N →∞ to the Cauchy distribution.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"415 1","pages":"59-85"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68829951","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}
{"title":"Positive fibered Lyapunov exponents for some quasi-periodically driven circle endomorphisms with critical points","authors":"Kristian Bjerklov, H. Eliasson","doi":"10.24033/ast.11104","DOIUrl":"https://doi.org/10.24033/ast.11104","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"415 1","pages":"181-193"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68830129","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}
{"title":"A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case","authors":"Raphael Beuzart-Plessis","doi":"10.24033/ast.11120","DOIUrl":"https://doi.org/10.24033/ast.11120","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"417 1","pages":"308"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68830268","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}
{"title":"Exposé Bourbaki 1161 : The Riemann zeta function in short intervals after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan","authors":"Adam J. Harper","doi":"10.24033/ast.1140","DOIUrl":"https://doi.org/10.24033/ast.1140","url":null,"abstract":"","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68831267","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}
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