Random strict partitions and determinantal point processes. (English) Zbl 1226.60072

Petrov, Leonid

Electron. Commun. Probab. 15, 162-175 (2010).

Summary: We present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice \(\{1,2,\dots\}\) or on the open half-line \((0,+\infty)\). The main result is the computation of the correlation kernels. They have integrable form and are expressed through the Euler gamma function (the lattice case) and the classical Whittaker functions (the continuous case). Our processes are obtained via a limit transition from a model of random strict partitions introduced by A. M. Borodin [J. Math. Sci., New York 96, No. 5, 3472–3477 (1999); translation from Zap. Nauchn. Semin. POMI 240, 44–52 (1997; Zbl 0938.43001)] in connection with the problem of harmonic analysis for projective characters of the infinite symmetric group.

MSC:

60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
20C25	Projective representations and multipliers

Keywords:

random strict partitions; determinantal point process; Macdonald kernel

Citations:

Zbl 0938.43001