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Published in:
2017 | OriginalPaper | Chapter
On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II
Authors : Thomas Bothner, Percy Deift, Alexander Its, Igor Krasovsky
Published in: Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics
Publisher: Springer International Publishing
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In this paper we continue our analysis [3] of the determinant det $$ ({I}- {\gamma}{K}_{s}), \ {\gamma} \ {\in} \ (0, 1)$$ where K s is the trace class operator acting in L2(−1, 1) with kernel $${K}_{s}(\lambda, \mu) = \frac{{\rm{sin}} \ {s}(\lambda-\mu)}{{\pi}(\lambda-\mu)}$$ . 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).