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

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)
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