Random normal matrices and Ward identities
Abstract
Consider the random normal matrix ensemble associated with a potential on the plane which is sufficiently strong near infinity. It is known that, to a first approximation, the eigenvalues obey a certain equilibrium distribution, given by Frostman's solution to the minimum energy problem of weighted logarithmic potential theory. On a finer scale, one can consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the correction to the expectation of fluctuations, and we prove that the potential field of the corrected fluctuations converge on smooth test functions to a Gaussian free field with free boundary conditions on the droplet associated with the potential.
Cite
@article{arxiv.1109.5941,
title = {Random normal matrices and Ward identities},
author = {Yacin Ameur and Haakan Hedenmalm and Nikolai Makarov},
journal= {arXiv preprint arXiv:1109.5941},
year = {2015}
}
Comments
An unnecessary line on p.3 removed. (The line also contained a type-o.)