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

2010/10/22 by Jinho Baik, Dong Wang, Baik, Jinho +1
Mathematics · #15B52 #41A60 (secondary) #60B20 (Primary) #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1010.4604

openalex publication_date 2010/10/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

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.

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