FLUCTUATIONS OF EIGENVALUES OF RANDOM NORMAL MATRICES

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

COMPLEX-MANIFOLDS

LIMIT

ZEROS

FUNCTIONALS

STATISTICS

MODEL

MATHEMATICS

MATEMATIK

Matematik

Publication and Content Type

ref (subject category)

art (subject category)