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The Poincare Inequality on the Hammi...

Stone, Yonathan Benjamin Edward,

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The Poincare Inequality on the Hamming Cube for Vector-Valued Functions /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The Poincare Inequality on the Hamming Cube for Vector-Valued Functions // Yonathan Benjamin Edward Stone.
作者:	Stone, Yonathan Benjamin Edward,
面頁冊數:	1 electronic resource (63 pages)
附註:	Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
Contained By:	Dissertations Abstracts International87-01B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32044254
ISBN:	9798288800801

The Poincare Inequality on the Hamming Cube for Vector-Valued Functions /
Stone, Yonathan Benjamin Edward,

The Poincare Inequality on the Hamming Cube for Vector-Valued Functions /Yonathan Benjamin Edward Stone. - 1 electronic resource (63 pages)

Source: Dissertations Abstracts International, Volume: 87-01, Section: B.

We study variations of and improvements to the classical Poincare inequality on the Hamming cube. The restriction to the discrete setting of the latter has neccessitated the development of many specialized techniques, including heat semigroup methods, hypercontractivity, and many other probabilistic ideas to address questions initially more rooted in analysis. This thesis covers a few such improvements including: 1. A complete characterization of Banach spaces for which a vector-valued variant of the KKL inequality holds, including partial work towards extending an improvement due to Talagrand to the same setting. 2. Improved bounds on the ratio and difference of L1 and L2 norms of sums of biased Rademacher random variables, with applications to various unanswered questions regarding the subject.

English

ISBN: 9798288800801Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

KKL inequality

The Poincare Inequality on the Hamming Cube for Vector-Valued Functions /
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500 $a Advisors: Ivanisvili, Paata Committee members: Vershynin, Roman; Solna, Knut; Hezari, Hamid.
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520 $a We study variations of and improvements to the classical Poincare inequality on the Hamming cube. The restriction to the discrete setting of the latter has neccessitated the development of many specialized techniques, including heat semigroup methods, hypercontractivity, and many other probabilistic ideas to address questions initially more rooted in analysis. This thesis covers a few such improvements including: 1. A complete characterization of Banach spaces for which a vector-valued variant of the KKL inequality holds, including partial work towards extending an improvement due to Talagrand to the same setting. 2. Improved bounds on the ratio and difference of L1 and L2 norms of sums of biased Rademacher random variables, with applications to various unanswered questions regarding the subject.
546 $a English
590 $a School code: 0030
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Statistics. $3 517247
650 4 $a Applied mathematics. $3 2122814
653 $a KKL inequality
653 $a Hamming cube
653 $a Rademacher random
653 $a Hypercontractivity
690 $a 0405
690 $a 0642
690 $a 0463
690 $a 0364
710 2 $a University of California, Irvine. $b Mathematics. $e degree granting institution. $3 3823182
720 1 $a Ivanisvili, Paata $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-01B.
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