Geometric Phenomena in High Dimensional ProbabilityDistributions
The proposed project lies at the cross-roads of Convex Geometry,
Probability Theory and the local theory of Banach spaces. We will
study large classes probability distributions of geometric origin on
spaces of a very high dimensio...
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Información proyecto GPHDPD
Líder del proyecto
TEL AVIV UNIVERSITY
No se ha especificado una descripción o un objeto social para esta compañía.
TRL
4-5
Presupuesto del proyecto
100K€
Fecha límite de participación
Sin fecha límite de participación.
Descripción del proyecto
The proposed project lies at the cross-roads of Convex Geometry,
Probability Theory and the local theory of Banach spaces. We will
study large classes probability distributions of geometric origin on
spaces of a very high dimension, tending to infinity. A particular,
important case is the uniform measure on an arbitrary
high-dimensional convex body. Even though the latter class of
probability distributions is quite diverse, we observe that some
non-trivial principles persist. For instance, any uniform measure on
a high-dimensional convex set necessarily has some approximately
gaussian marginals. The recent years have seen progress in the
analysis of such high-dimensional measures. The proposed project
intends to deepen and extend these first signs of understanding, to
contribute towards a comprehensive theory of convexity-related
measures, and to develop new methods for the study of
high-dimensional distributions in general.