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Global fluctuations...
Abstract
Ämnesord
Stäng
- 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
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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