On the traces of Laguerre processes. (English) Zbl 1190.60098

Perez-Abreu, Victor; Tudor, Constantin

Electron. J. Probab. 14, 2241-2263 (2009).

Summary: Almost sure and \(L^{k}\)-convergence of the traces of Laguerre processes to the family of dilations of the standard free Poisson distribution are established. We also prove that the fluctuations around the limiting process, converge weakly to a continuous centered Gaussian process. The almost sure convergence on compact time intervals of the largest and smallest eigenvalues processes is also established

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60F05	Central limit and other weak theorems
60F25	\(L^p\)-limit theorems
60B20	Random matrices (probabilistic aspects)

Keywords:

matrix valued process; complex Wishart distribution; trace processes; largest and smallest eigenvalues; propagation of chaos; fluctuations of moments; free Poisson distribution