Sharp deviation bounds for quadratic forms

Abstract: This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector (\xiv) with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The results are stated under general conditions and do not suppose any special structure of the vector (\xiv). The obtained bounds are exact (non-asymptotic), all constants are explicit and the leading terms in the bounds are sharp.