## Asymptotics of Plancherel measures for the infinite-dimensional unitary group.(English)Zbl 1153.60058

Summary: We study a two-dimensional family of probability measures on infinite Gelfand-Tsetlin schemes induced by a distinguished family of extreme characters of the infinite-dimensional unitary group. These measures are unitary group analogs of the well-known Plancherel measures for symmetric groups.
We show that any measure from our family defines a determinantal point process on $$\mathbb Z_+ \times \mathbb Z$$, and we prove that in appropriate scaling limits, such processes converge to two different extensions of the discrete sine process as well as to the extended Airy and Pearcey processes.

### MSC:

 60K40 Other physical applications of random processes 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
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### References:

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