INFINITE DETERMINANTAL MEASURES AND THE ERGODIC DECOMPOSITION OF INFINITE PICKRELL MEASURES - Ecole Centrale de Marseille Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

INFINITE DETERMINANTAL MEASURES AND THE ERGODIC DECOMPOSITION OF INFINITE PICKRELL MEASURES

Alexander I. Bufetov

Résumé

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.
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Dates et versions

hal-00933357 , version 1 (20-01-2014)

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  • HAL Id : hal-00933357 , version 1

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