BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Two-sided moment estimates for random chaoses. Meller, Rafal


Let $X_1,\ldots,X_n$ be random variables such that there exists a constant $C>1$ satisfying $\|X_i\|_{2p} \leq C \|X_i\|_p$ for every $p \geq 1$. We define random chaos $S=\sum a_{i_1,...,i_d} X_{i_1}\cdots X_{i_d}$. We will show two-sided deterministic bounds on $||S||_p$, with constant depending only on $C$ and $d$ in two cases: 1) $X_1,\ldots,X_n$ are nonnegative and $a_{i_1,...,i_d}\geq 0$. 2) $X_1,\ldots ,X_n$ are symmetric, $d=2$.

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