Mathematics – Metric Geometry
Scientific paper
2005-01-22
Geometric aspects of functional analysis (Israel Seminar 2004 -- 2005), pp. 271--295, Lecture Notes in Math., 1910, Springer,
Mathematics
Metric Geometry
30 pages; typos and minor errors corrected
Scientific paper
If the Euclidean norm is strongly concentrated with respect to a measure, the average distribution of an average marginal of this measure has Gaussian asymptotics that captures tail behaviour. If the marginals of the measure 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.
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