This is an announcement for the paper "Tail-sensitive Gaussian asymptotics for marginals of concentrated measures in high dimension" by Sasha Sodin. Abstract: 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. Archive classification: Metric Geometry; Functional Analysis Remarks: 29 pages The source file(s), all3.tex: 62865 bytes, is(are) stored in gzipped form as 0501382.gz with size 19kb. The corresponding postcript file has gzipped size 96kb. Submitted from: a_sodin@hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0501382 or http://arXiv.org/abs/math.MG/0501382 or by email in unzipped form by transmitting an empty message with subject line uget 0501382 or in gzipped form by using subject line get 0501382 to: math@arXiv.org.