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Springer2014,Superconcentration and Related topics pdf Sourav Chatterjee

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  • TA的每日心情
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    2016-3-19 06:18
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    [LV.4]偶尔看看III

    发表于 2015-9-14 19:31:19 | 显示全部楼层 |阅读模式
    Superconcentration and Related Topics (Springer Monographs in Mathematics)pdf, 2014
    by Sourav Chatterjee


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    A certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple valleys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach.

    Understanding the fluctuations of random objects is one of the major goals of probability theory and a whole subfield of probability and analysis, called concentration of measure, is devoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations of very complicated random variables. Usually, concentration of measure is useful when more direct problem-specific approaches fail; as a result, it has massively gained acceptance over the last forty years. And yet, there is a large class of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substantial contribution of this book, which developed from a set of six lectures the author first held at the Cornell Probability Summer School in July 2012.

    The book is interspersed with a sizable number of open problems for professional mathematicians as well as exercises for graduate students working in the fields of probability theory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability.


    斯坦福大牛Sourav Chatterjee写的关于Stein's method和Concentration inequalities的专著。作者05年斯坦福博士毕业,师从Persi Diaconis,Chatterjee在Annals of Mathematics,Annals of Probability,Annals of Statistics等顶尖杂志发过论文。

    Persi Diaconis,1945年1月31日-,斯坦福数学与统计学教授,曾为职业魔术师。他是斯坦福大学的数学与统计学教授。他解决了一些随机性的问题,包括掷币和洗牌。1992年,他和David Bayer证明完美的洗牌至少要洗七次。他又和的Richard Montgomery合作说明从高处跌下的猫为何总能以脚着地,证明了掷币哪面向上,物理因素比运气重要得多。著有《群表示论在统计中的应用》《魔术数学》 。相关阅读斯坦福大学的数学与统计学教授Persi Diaconis访谈

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  • TA的每日心情
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    2016-7-6 23:05
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    [LV.3]偶尔看看II

    发表于 2015-11-27 22:01:32 | 显示全部楼层
    very good, thanks!!
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  • TA的每日心情
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    2017-12-15 11:07
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    [LV.7]常住居民III

    发表于 2016-2-13 13:49:39 | 显示全部楼层
    谢谢楼主辛苦分享!!
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