Fluctuations of eigenvalues of random normal matrices

By Y. Ameur, H. Hedenmalm, Nikolai G. Makarov. 2008

187 citations recorded by the source corpus.

In this article, we consider a fairly general potential in the plane and the corresponding Boltzmann-Gibbs distribution of eigenvalues of random normal matrices. As the order of the matrices tends to infinity, the eigenvalues condensate on a certain compact subset of the plane—the “droplet.” We prove that fluctuations of linear statistics of eigenvalues of random normal matrices converge on compact subsets of the interior of the droplet to a Gaussian field, and we discuss various ramifications of this result.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9a8347bd9c27ff0e2fc6b5800b1f07c6c765e753

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Berezin transform in polynomial bergman spaces (2008, background): “The relevant results for our applications in [1] are primarily theorems 2.”
Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals (2013, background): “probability literature, such questions are now understood in dimension 2 for the particular determinantal case ˇ D 2 [2, 3] and in dimension 1 with the logarithmic interaction [11, 12, 78].”
Monte Carlo with determinantal point processes (2016, unknown): “…1997, 1998, Diaconis and Evans, 2001, Soshnikov, 2002, Pastur, 2006, Rider and Virág, 2007, Popescu, 2009, Kriecherbauer and Shcherbina, 2010, Ameur et al., 2011, 2015, Berman, 2012, Shcherbina, 2013, Breuer and Duits, 2013, 2014, Johansson and Lambert, 2015, Lambert, 2015a,b] for a…”