Small ball probability estimates for log-concave measures Academic Article uri icon

abstract

  • We establish a small ball probability inequality for isotropic logconcave probability measures: there exist absolute constants c1, c2 > 0 such that if X is an isotropic log-concave random vector in Rn with ψ2 constant and bounded by b and if A is a non-zero nxn matrix, then for every ε Ie{cyrillic, ukrainian} (0, c1) and y Ie{cyrillic, ukrainian} Rn,= where c1, c2 > 0 are absolute constants. © 2011 American Mathematical Society.

author list (cited authors)

  • Paouris, G.

citation count

  • 44

publication date

  • June 2011