On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II

Abstract

In this paper we continue our analysis [3] of the determinant det(I− γKs), γ ∈ (0, 1) where Ks is the trace class operator acting in L2(−1, 1) with kernel Ks(λ, μ) = (Formula Present). In [3] various key asymptotic results were stated and utilized, but without proof: Here we provide the proofs (see Theorem 1.2 and Proposition 1.3 below).