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Probabilistic Symmetrization Inequalities from a Combinatorial Point of View

Tuesday, March 3, 2015 - 2:00pm - 3:00pm
Lind 305
Jiange Li (University of Delaware)
We consider certain symmetrization inequalities relating the probabilities that the sum and difference of two i.i.d. random variables lie in certain measurable sets. There are close connections between optimal constants in such estimates and some problems in combinatorial geometry and extremal graph theory, such as the kissing number problem and Tur\'{a}n theorem for triangle-free graph. As regards applications, such estimates are used to develop H\{o}lder-type and reverse H\{o}lder-type inequalities for certain class of random variables.