Random matrices in 2D, Laplacian growth and operator theory

Mark Mineev-Weinstein, Mihai Putinar, Razvan Teodorescu
2008 Journal of Physics A: Mathematical and Theoretical  
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
more » ... 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.
doi:10.1088/1751-8113/41/26/263001 fatcat:ym43zdptdzhqfmlaiwlkt3ijee