INFINITE DETERMINANTAL MEASURES AND THE ERGODIC DECOMPOSITION OF INFINITE PICKRELL MEASURES

Alexander I. Bufetov (1)

1 Mathématiques Fondamentales

The main result of this paper, Theorem 1.11, gives an explicit description of the ergodic decomposition for infinite Pickrell measures on spaces of infinite complex matrices. The main construction is that of sigma-finite analogues of determinantal measures on spaces of configurations. An example is the infinite Bessel point process, the scaling limit of sigma-finite analogues of Jacobi orthogonal polynomial ensembles. The statement of Theorem 1.11 is that the infinite Bessel point process (subject to an appropriate change of variables) is precisely the ergodic decomposition measure for infinite Pickrell measures.

Mots clés: ergodic decomposition; Pickrell measures; infinite determinantal measures; orthogonal polynomial ensembles

Domaines: Systèmes dynamiques [math.DS]; Théorie des représentations [math.RT]

Alexander I. Bufetov. INFINITE DETERMINANTAL MEASURES AND THE ERGODIC DECOMPOSITION OF INFINITE PICKRELL MEASURES. 2013. ⟨hal-00933357⟩