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Geometric Phenomena in High-Dimensional Probability Distributions (GPHDPD)
Start date: Apr 1, 2009, End date: Mar 31, 2013 PROJECT  FINISHED 

"The proposed project lies at the cross-roads of Convex Geometry,Probability Theory and the local theory of Banach spaces. We willstudy large classes probability distributions of geometric origin onspaces of a very high dimension, tending to infinity. A particular,important case is the uniform measure on an arbitraryhigh-dimensional convex body. Even though the latter class ofprobability distributions is quite diverse, we observe that somenon-trivial principles persist. For instance, any uniform measure ona high-dimensional convex set necessarily has some approximatelygaussian marginals. The recent years have seen progress in theanalysis of such high-dimensional measures. The proposed projectintends to deepen and extend these first signs of understanding, tocontribute towards a comprehensive theory of convexity-relatedmeasures, and to develop new methods for the study ofhigh-dimensional distributions in general."
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