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Bulk scaling limit of the Laguerre ensemble. (English) Zbl 1225.60015
Summary: We consider the \(\beta\)-Laguerre ensemble, a family of distributions generalizing the joint eigenvalue distribution of the Wishart random matrices. We show that the bulk scaling limit of these ensembles exists for all \(\beta>0\) for a general family of parameters, and it is the same as the bulk scaling limit of the corresponding \(\beta\)-Hermite ensemble.

MSC:
60B20 Random matrices (probabilistic aspects)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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