Global fluctuations in general β Dyson’s Brownian motion
2008 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, Vol. 118, no 6, 1022-1042 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2008. Vol. 118, no 6, 1022-1042 p.
central limit theorem; Dyson's Brownian motion; interacting diffusion; random matrices; RANDOM MATRICES; EIGENVALUES; PARTICLES; LIMIT; CLT; LAW
IdentifiersURN: urn:nbn:se:kth:diva-8639DOI: 10.1016/j.spa.2007.07.010ISI: 000256599800008ScopusID: 2-s2.0-42649108381OAI: oai:DiVA.org:kth-8639DiVA: diva2:14015
QC 201007052008-06-042008-06-042010-07-05Bibliographically approved