Concentration inequalities for polynomials in α-sub-exponential random variables

We derive multi-level concentration inequalities for polynomials in independent random variables with an α-sub-exponential tail decay. A particularly interesting case is given by quadratic forms f(X1,…,Xn)=⟨X,AX⟩, which we prove Hanson–Wright-type explicit dependence on various norms of the matrix A. consequence these a two-level inequality variables, such as Poisson chaos. provide applications inequalities. Among them are generalizations some results proven Rudelson and Vershynin from sub-Gaussian to i. e. Euclidean norm linear image vector distance between fixed subspace.