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

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We study the partition function Z of a Coulomb gas of particles with an external potential 2v applied to the particles in an interval of length L. When v is infinite, Z describes the gap probability for GUE eigenvalues in the bulk scaling limit, and has been well-studied for many years. Here we study the the behavior of Z in the full (v,L) plane.

Percy Deift (NYU) is the LMS Hardy Lecturer this year, and will be speaking in Cambridge on July 2nd at 1pm in Mill Lane Lecture Room 1.

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