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The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities. (English) Zbl 1021.60018

Summary: We discuss the CLT for the global and local linear statistics of random matrices from classical compact groups. The main parts of our proofs are certain combinatorial identities, much in the spirit of works by M. Kac [Duke Math. J. 21, 501-509 (1954; Zbl 0056.10201)] and H. Spohn [in: Hydrodynamic behavior and interacting particle systems. IMA Vol. Math. Appl. 9, 151-179 (1987; Zbl 0674.60096)].

MSC:

60F05 Central limit and other weak theorems
15B52 Random matrices (algebraic aspects)
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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