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.
Sharp deviation bounds for midpoint and endpoint of geodesics in exponential last passage percolation
Sharp deviation bounds and concentration phenomenon for the squared norm of a sub-gaussian vector
Comparison and anti-concentration bounds for maxima of Gaussian random vectors
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