153 citations · 544 across the 20 of their papers we have counts for
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Scaling limits of random normal matrix processes at singular boundary points
Yacin Ameur, Nam-Gyu Kang, Nikolai Makarov +1
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…
Rescaling Ward identities in the random normal matrix model
Yacin Ameur, Nam-Gyu Kang, Nikolai Makarov
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…
Radial SLE martingale-observables
Nam-Gyu Kang, Nikolai Makarov
We implement a version of radial conformal field theory in a family of statistical fields generated by central charge modification of the Gaussian free field and show that the corr…
Coulomb gas ensembles and Laplacian growth
Haakan Hedenmalm, Nikolai Makarov
We consider the normal matrix ensemble under a general confining potential. We find that the eigenvalues condensate on a compact set in the plane, which we call the spectral drople…
Gaussian free field and conformal field theory
Nam-Gyu Kang, Nikolai Makarov
In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical…
Fluctuations of eigenvalues of random normal matrices
Yacin Ameur, Haakan Hedenmalm, Nikolai Makarov
In this note, we prove Gaussian field convergence of fluctuations of eigenvalues of random normal matrices in the interior of a quantum droplet.