Small ball probability estimates for log-concave measures
نویسنده
چکیده
We establish a small ball probability inequality for isotropic log-concave probability measures: there exist absolute constants c1, c2 > 0 such that if X is an isotropic log-concave random vector in R with ψ2 constant bounded by b and if A is a non-zero n × n matrix, then for every ε ∈ (0, c1) and y ∈ R, P (‖Ax− y‖2 6 ε‖A‖HS) 6 ε ` c2 b ‖A‖HS ‖A‖op ́2 , where c1, c2 > 0 are absolute constants.
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