TY - GEN

T1 - Tail-sensitive Gaussian asymptotics for marginals of concentrated measures in high dimension

AU - Sodin, S.

PY - 2007

Y1 - 2007

N2 - If the Euclidean norm | · | is strongly concentrated with respect to a measure μ, the average distribution of an average marginal of μ has Gaussian asymptotics that captures tail behaviour. If the marginals of μ have exponential moments, Gaussian asymptotics for the distribution of the average marginal implies Gaussian asymptotics for the distribution of most individual marginals. We show applications to measures of geometric origin.

AB - If the Euclidean norm | · | is strongly concentrated with respect to a measure μ, the average distribution of an average marginal of μ has Gaussian asymptotics that captures tail behaviour. If the marginals of μ have exponential moments, Gaussian asymptotics for the distribution of the average marginal implies Gaussian asymptotics for the distribution of most individual marginals. We show applications to measures of geometric origin.

UR - http://www.scopus.com/inward/record.url?scp=34247625637&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-72053-9_16

DO - 10.1007/978-3-540-72053-9_16

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AN - SCOPUS:34247625637

SN - 3540720529

SN - 9783540720522

T3 - Lecture Notes in Mathematics

SP - 271

EP - 295

BT - Geometric Aspects of Functional Analysis

PB - Springer Verlag

ER -