244 research outputs found
Rescaling Ward identities in the random normal matrix model
We study existence and universality of scaling limits for the eigenvalues of
a random normal matrix, in particular at points on the boundary of the
spectrum. Our approach uses Ward's equation, which is an identity satisfied by
the 1-point function.Comment: This is a substantial revision with several new results. The previous
section 7 on singular boundary points has been lifted out and developed in a
separate not
Scaling limits of random normal matrix processes at singular boundary points
We give a method for taking microscopic limits of normal matrix ensembles. We
apply this method to study the behaviour near certain types of singular points
on the boundary of the droplet. Our investigation includes ensembles without
restrictions near the boundary, as well as hard edge ensembles, where the
eigenvalues are confined to the droplet. We establish in both cases existence
of new types of determinantal point fields, which differ from those which can
appear at a regular boundary point, or in the bulk.Comment: This (final) version contains some improvements with respect to
presentation, correction of typos, and so o
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