Abstract
Consider a setA of symmetricn×n matricesa=(ai,j)i,j≤n. Consider an independent sequence (gi)i≤n of standard normal random variables, and letM=Esupa∈A|Σi,j⪯nai,jgigj|. Denote byN2(A, α) (resp.Nt(A, α)) the smallest number of balls of radiusα for thel2 norm ofRn2 (resp. the operator norm) needed to coverA. Then for a universal constantK we haveα(logN2(A, α))1/4≤KM. This inequality is best possible. We also show that forδ≥0, there exists a constantK(δ) such thatα(logNt≤K(δ)M.
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