Global fluctuations in general β Dyson’s Brownian motion

• We consider a system of diffusing particles on the real line in a quadratic external potential and with a logarithmic interaction potential. The empirical measure process is known to converge weakly to a deterministic measure-valued process as the number of particles tends to infinity. Provided the initial fluctuations are small, the rescaled linear statistics of the empirical measure process converge in distribution to a Gaussian limit for sufficiently smooth test functions. For a large class of analytic test functions, we derive explicit general formulae for the mean and covariance in this central limit theorem by analyzing a partial differential equation characterizing the limiting fluctuations.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

central limit theorem; Dyson's Brownian motion; interacting diffusion; random matrices; RANDOM MATRICES; EIGENVALUES; PARTICLES; LIMIT; CLT; LAW

MATHEMATICS

MATEMATIK

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