Concentration of permanent estimators for certain large matrices

الأصل · EN

Let Aₙ=(aij)ᵢ,ⱼ₌₁ⁿ be an n× n positive matrix with entries in [a,b], 0<a≤ b. Let Xₙ=()ᵢ,ⱼ₌₁ⁿ be a random matrix, where xij are i.i.d. N(0,1) random variables. We show that for large n, (XₙᵗXₙ) concentrates sharply at the permanent of Aₙ, in the sense that n⁻¹ ((XₙᵗXₙ)/perAₙ)→ₙ→∞0 in probability.