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Vector-Valued Concentration Inequalities on Discrete Spaces
Vector-Valued Concentration Inequalities on Discrete Spaces
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202104639
- ISBN
- 9798293894451
- DDC
- 510
- 저자명
- Gordin, Miriam.
- 서명/저자
- Vector-Valued Concentration Inequalities on Discrete Spaces
- 발행사항
- [Sl] : Princeton University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 89 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-04, Section: A.
- 주기사항
- Advisor: van Handel, Ramon.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2025.
- 초록/해제
- 요약Existing concentration inequalities for functions that take values in a general Banach space, such as the classical results of Pisier (1986) and the more recent contribution of Ivanisvili, van Handel, and Volberg (2020), are known only in very special settings, such as the Gaussian measure on Rn and the uniform measure on the discrete cube {−1, 1}n.In this thesis, we prove such vector-valued concentration inequalities for more general probability measures on discrete spaces. In the first chapter, we present such an inequality for the biased product measure on the discrete cube with an optimal dependence on the bias parameter and the Rademacher type of the target Banach space. This result yields scaling limits to the product of Poisson measures, as well as lower bounds on the average distortion of embeddings of the discrete cube into Banach spaces of nontrivial type, implying average nonembeddability.Moreover, we present a novel vector-valued concentration inequality for the uniform measure on the symmetric group, which is the first to go beyond the setting of product measures. Our inequality attains optimal dimensional dependency for Banach space of Rademacher type p ∈ [1, 2), which implies average nonembeddability of the symmetric group into Banach spaces of nontrivial Rademacher type. Our approach enriches the Markov semigroup interpolation argument used by Ivanisvili, van Handel, and Volberg. In particular, we further techniques for capturing the concentration of random coefficients arising from the semigroup method.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Mathematics education
- 키워드
- Banach space
- 키워드
- Gaussian measure
- 기타저자
- Princeton University Applied and Computational Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-04A.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798293894451
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aGordin, Miriam.▼0(orcid)0000-0002-0767-2366
■24510▼aVector-Valued Concentration Inequalities on Discrete Spaces
■260 ▼a[Sl]▼bPrinceton University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a89 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-04, Section: A.
■500 ▼aAdvisor: van Handel, Ramon.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2025.
■520 ▼aExisting concentration inequalities for functions that take values in a general Banach space, such as the classical results of Pisier (1986) and the more recent contribution of Ivanisvili, van Handel, and Volberg (2020), are known only in very special settings, such as the Gaussian measure on Rn and the uniform measure on the discrete cube {−1, 1}n.In this thesis, we prove such vector-valued concentration inequalities for more general probability measures on discrete spaces. In the first chapter, we present such an inequality for the biased product measure on the discrete cube with an optimal dependence on the bias parameter and the Rademacher type of the target Banach space. This result yields scaling limits to the product of Poisson measures, as well as lower bounds on the average distortion of embeddings of the discrete cube into Banach spaces of nontrivial type, implying average nonembeddability.Moreover, we present a novel vector-valued concentration inequality for the uniform measure on the symmetric group, which is the first to go beyond the setting of product measures. Our inequality attains optimal dimensional dependency for Banach space of Rademacher type p ∈ [1, 2), which implies average nonembeddability of the symmetric group into Banach spaces of nontrivial Rademacher type. Our approach enriches the Markov semigroup interpolation argument used by Ivanisvili, van Handel, and Volberg. In particular, we further techniques for capturing the concentration of random coefficients arising from the semigroup method.
■590 ▼aSchool code: 0181.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aMathematics education
■653 ▼aBanach space
■653 ▼aMarkov semigroup interpolation argument
■653 ▼aGaussian measure
■690 ▼a0405
■690 ▼a0642
■690 ▼a0280
■71020▼aPrinceton University▼bApplied and Computational Mathematics.
■7730 ▼tDissertations Abstracts International▼g87-04A.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17358293▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
