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ItemConcentration and Convexity - Part 1(Georgia Institute of Technology, 2019-12-10) Paouris, GrigorisThe Concentration of measure phenomenon is a fundamental tool of high dimensional probability and of Asymptotic Geometric Analysis. Independence or Isoperimetry are two typical reasons for the appearance of this phenomenon. In these talks I will introduce the phenomenon and I will show how High dimensional Geometry affects the concentration. In particular I will explain how "convexity" can be used to establish strong concentration inequalities in the Gauss space and how the "convexity" of the underline measure is responsible for deviation principles.
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ItemConcentration and Convexity - Part 2(Georgia Institute of Technology, 2019-12) Paouris, GrigorisThe Concentration of measure phenomenon is a fundamental tool of high dimensional probability and of Asymptotic Geometric Analysis. Independence or Isoperimetry are two typical reasons for the appearance of this phenomenon. In these talks I will introduce the phenomenon and I will show how High dimensional Geometry affects the concentration. In particular I will explain how "convexity" can be used to establish strong concentration inequalities in the Gauss space and how the "convexity" of the underline measure is responsible for deviation principles.
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ItemConcentration and Convexity - Part 3(Georgia Institute of Technology, ) Paouris, GrigorisThe Concentration of measure phenomenon is a fundamental tool of high dimensional probability and of Asymptotic Geometric Analysis. Independence or Isoperimetry are two typical reasons for the appearance of this phenomenon. In these talks I will introduce the phenomenon and I will show how High dimensional Geometry affects the concentration. In particular I will explain how "convexity" can be used to establish strong concentration inequalities in the Gauss space and how the "convexity" of the underline measure is responsible for deviation principles.