On the largest eigenvalue of a Hermitian random matrix model with spiked external source I. Rank one case

Details On the largest eigenvalue of a Hermitian random matrix model with spiked external source I. Rank one case On the largest eigenvalue of a Hermitian random matrix model with spiked external source I. Rank one case

2010-10-22

arxiv.org/abs/1010.4604v2

Physics

Mathematical Physics

61 pages, 10 figures, typos corrected

Scientific paper

Consider a Hermitian matrix model under an external potential with spiked external source. When the external source is of rank one, we compute the limiting distribution of the largest eigenvalue for general, regular, analytic potential for all values of the external source. There is a transitional phenomenon, which is universal for convex potentials. However, for non-convex potentials, new types of transition may occur. The higher rank external source is analyzed in the subsequent paper.

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