Concentration inequalities for polynomials in $\alpha$-sub-exponential random variables

Understand

In this work we derive multi-level concentration inequalities for polynomial functions in independent random variables with a $\alpha$-sub-exponential tail decay.

• A particularly interesting case is given by quadratic forms $f(X_1, \ldots, X_n) = \langle X,A X \rangle$, for which we prove Hanson-Wright-type inequalities with explicit dependence on various norms of the matrix $A$.
• A consequence of these inequalities is a two-level concentration inequality for quadratic forms in $\alpha$-sub-exponential random variables, such as quadratic Poisson chaos.
• We provide various applications of these inequalities.