Random matrices and Laplacian growth
Mathematical Physics
2009-07-29 v1 math.MP
Abstract
The theory of random matrices with eigenvalues distributed in the complex plane and more general "beta-ensembles" (logarithmic gases in 2D) is reviewed. The distribution and correlations of the eigenvalues are investigated in the large N limit. It is shown that in this limit the model is mathematically equivalent to a class of diffusion-controlled growth models for viscous flows in the Hele-Shaw cell and other growth processes of Laplacian type. The analytical methods used involve the technique of boundary value problems in two dimensions and elements of the potential theory.
Cite
@article{arxiv.0907.4929,
title = {Random matrices and Laplacian growth},
author = {A. Zabrodin},
journal= {arXiv preprint arXiv:0907.4929},
year = {2009}
}
Comments
20 pages, 2 figures, a contribution to the Oxford Handbook of Random Matrix Theory