Random Matrices in 2D, Laplacian Growth and Operator Theory - Nonlinear Sciences > Exactly Solvable and Integrable SystemsReport as inadecuate




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Abstract: Since it was first applied to the study of nuclear interactions by Wigner andDyson, almost 60 years ago, Random Matrix Theory RMT has developed into afield of its own within applied mathematics, and is now essential to many partsof theoretical physics, from condensed matter to high energy. The fundamentalresults obtained so far rely mostly on the theory of random matrices in onedimension the dimensionality of the spectrum, or equilibrium probabilitydensity. In the last few years, this theory has been extended to the casewhere the spectrum is two-dimensional, or even fractal, with dimensions between1 and 2. In this article, we review these recent developments and indicate somephysical problems where the theory can be applied.



Author: Mark Mineev-Weinstein, Mihai Putinar, Razvan Teodorescu

Source: https://arxiv.org/







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