English

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

Mathematical Physics 2010-12-21 v2 Classical Analysis and ODEs math.MP Probability

Abstract

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.

Keywords

Cite

@article{arxiv.1010.4604,
  title  = {On the largest eigenvalue of a Hermitian random matrix model with spiked external source I. Rank one case},
  author = {Jinho Baik and Dong Wang},
  journal= {arXiv preprint arXiv:1010.4604},
  year   = {2010}
}

Comments

61 pages, 10 figures, typos corrected

R2 v1 2026-06-21T16:32:33.630Z