September

Krzysztof Oleszkiewicz (University Warsaw): On the asymptotics of the optimal constants in the Khinchine-Kahane inequality

Let us consider a sequence of indepenedent symmetric +/-1 random variables, often called the Rademacher system. A linear combination of these random variables is a real random variable called a (weighted) Rademacher sum. There are also vector-valued Rademacher sums, in which the real coefficients in the linear combination are replaced by vectors from some normed linear space. Rademacher sums, both real and vector-valued, have been studied for more than 100 years now. In the talk, classical moment inequalities for Rademacher sums will be described, going back to Khinchine (1923) and Kahane (1964), as well as some more recent results.