A ug 2 00 4 LARGE n LIMIT OF GAUSSIAN RANDOM MATRICES WITH EXTERNAL SOURCE , PART II

Abstract

We continue the study of the Hermitian random matrix ensemble with external source 1 Z n e −nTr(1 2 M 2 −AM) dM where A has two distinct eigenvalues ±a of equal multiplicity. This model exhibits a phase transition for the value a = 1, since the eigenvalues of M accumulate on two intervals for a > 1, and on one interval for 0 < a < 1. The case a > 1 was… (More)

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