The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures

Alexander I. Bufetov (1, 2, 3, 4) , Yanqi Qiu (1)

1 I2M - Institut de Mathématiques de Marseille
2 SMI | RAS - Steklov Mathematical Institute [Moscow]
3 Institute for Information Transmission Problems
4 HSE - Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow]

The main result of this paper, Theorem 1.1, gives explicit formulae for the kernels of the ergodic decomposition measures for infinite Pickrell measures on spaces of infinite complex matrices. The kernels are obtained as the scaling limits of Christoffel-Uvarov deformations of Jacobi orthogonal polynomial ensembles.

Mots clés: Pickrell measures; ergodic decompositions; determinantal measures; Jacobi orthogonal polynomial ensembles; scaling limits

Domaines: Analyse fonctionnelle [math.FA]; Systèmes dynamiques [math.DS]; Probabilités [math.PR]; Théorie des représentations [math.RT]

Alexander I. Bufetov, Yanqi Qiu. The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures. Arkiv för Matematik, 2016, 54 (2), pp.403 - 435. ⟨10.1007/s11512-016-0230-x⟩. ⟨hal-00957661⟩