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

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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).

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Bothner, T., Deift, P., Its, A., & Krasovsky, I. (2017). On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II. In Operator Theory: Advances and Applications (Vol. 259, pp. 213–234). Springer International Publishing. https://doi.org/10.1007/978-3-319-49182-0_12

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