2008/05/04 by Mark Mineev-Weinstein, Mihai Putinar, Razvan Teodorescu
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics #cond-mat.mes-hall #cond-mat.soft #math-ph #math.MP #nlin.PS #nlin.SI
paper · pdf · doi:10.1088/1751-8113/41/26/263001
published as J. Phys. A: Math. Theor. 41 (2008) 263001 · 88 pages, 8 figures
arxiv created 2008/05/04 · openalex publication_date 2008/06/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of theoretical physics, from condensed matter to high energy. The fundamental results obtained so far rely mostly on the theory of random matrices in one dimension (the dimensionality of the spectrum, or equilibrium probability density). In the last few years, this theory has been extended to the case where the spectrum is two-dimensional, or even fractal, with dimensions between 1 and 2. In this article, we review these recent developments and indicate some physical problems where the theory can be applied.