1998/10/31 by Paul Zinn-Justin, P. Zinn-Justin
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Random Matrices and Applications #Stochastic processes and statistical mechanics #cond-mat #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physreve.59.4884
published as Phys. Rev. E59 #5 (1999), 4884 · 11 pages, harvmac. revised x 2: refs and minor comments added
arxiv created 1999/01/14 · openalex publication_date 1999/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we give an elementary proof of the additivity of the functional inverses of the resolvents of large N random matrices, using recently developed matrix model techniques. This proof also gives a very natural generalization of these formulas to the case of measures with an external field. A similar approach yields a relation of the same type for multiplication of random matrices.