Pub Date : 2013-12-17DOI: 10.1007/S11511-013-0103-0
N. Karpenko, Maksim Zhykhovich
{"title":"Isotropy of unitary involutions","authors":"N. Karpenko, Maksim Zhykhovich","doi":"10.1007/S11511-013-0103-0","DOIUrl":"https://doi.org/10.1007/S11511-013-0103-0","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"211 1","pages":"227-253"},"PeriodicalIF":3.7,"publicationDate":"2013-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11511-013-0103-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53063346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-12-17DOI: 10.1007/S11511-013-0106-X
Kunrui Yu
{"title":"p-adic logarithmic forms and a problem of Erdős","authors":"Kunrui Yu","doi":"10.1007/S11511-013-0106-X","DOIUrl":"https://doi.org/10.1007/S11511-013-0106-X","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"10 1","pages":"315-382"},"PeriodicalIF":3.7,"publicationDate":"2013-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11511-013-0106-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53063587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-10-22DOI: 10.1007/S11511-013-0099-5
A. Chermak
{"title":"Fusion systems and localities","authors":"A. Chermak","doi":"10.1007/S11511-013-0099-5","DOIUrl":"https://doi.org/10.1007/S11511-013-0099-5","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"211 1","pages":"47-139"},"PeriodicalIF":3.7,"publicationDate":"2013-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11511-013-0099-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53062805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We determine the asymptotics of the independence number of the random d-regular graph for all $${dgeq d_0}$$d≥d0. It is highly concentrated, with constant-order fluctuations around $${nalpha_*-c_*log n}$$nα∗-c∗logn for explicit constants $${alpha_*(d)}$$α∗(d) and $${c_*(d)}$$c∗(d). Our proof rigorously confirms the one-step replica symmetry breaking heuristics for this problem, and we believe the techniques will be more broadly applicable to the study of other combinatorial properties of random graphs.
{"title":"Maximum independent sets on random regular graphs","authors":"Jian Ding, A. Sly, Nike Sun","doi":"10.14288/1.0044424","DOIUrl":"https://doi.org/10.14288/1.0044424","url":null,"abstract":"We determine the asymptotics of the independence number of the random d-regular graph for all $${dgeq d_0}$$d≥d0. It is highly concentrated, with constant-order fluctuations around $${nalpha_*-c_*log n}$$nα∗-c∗logn for explicit constants $${alpha_*(d)}$$α∗(d) and $${c_*(d)}$$c∗(d). Our proof rigorously confirms the one-step replica symmetry breaking heuristics for this problem, and we believe the techniques will be more broadly applicable to the study of other combinatorial properties of random graphs.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"217 1","pages":"263-340"},"PeriodicalIF":3.7,"publicationDate":"2013-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66895698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-06-25DOI: 10.1007/S11511-013-0097-7
T. Tao, T. Ziegler
{"title":"Erratum to “The primes contain arbitrarily long polynomial progressions”","authors":"T. Tao, T. Ziegler","doi":"10.1007/S11511-013-0097-7","DOIUrl":"https://doi.org/10.1007/S11511-013-0097-7","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"210 1","pages":"403-404"},"PeriodicalIF":3.7,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11511-013-0097-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53062952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-06-06DOI: 10.1007/S11511-016-0136-2
N. Bergeron, J. Millson, C. Moeglin
{"title":"The Hodge conjecture and arithmetic quotients of complex balls","authors":"N. Bergeron, J. Millson, C. Moeglin","doi":"10.1007/S11511-016-0136-2","DOIUrl":"https://doi.org/10.1007/S11511-016-0136-2","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"216 1","pages":"1-125"},"PeriodicalIF":3.7,"publicationDate":"2013-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11511-016-0136-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53064553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-05-08DOI: 10.1007/S11511-016-0132-6
Pramod N. Achar, L. Rider
{"title":"Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture","authors":"Pramod N. Achar, L. Rider","doi":"10.1007/S11511-016-0132-6","DOIUrl":"https://doi.org/10.1007/S11511-016-0132-6","url":null,"abstract":"","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":"1 1","pages":"183-216"},"PeriodicalIF":3.7,"publicationDate":"2013-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S11511-016-0132-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53064331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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