Infinite Determinantal Measures and The Ergodic Decomposition of Infinite Pickrell Measures II. Convergence of determinantal measures

Abstract

The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of probability measures on the space of configurations, we also consider the weak topology on the space of finite measures on the space of finite measures on the half-line, used via the natural immersion, well-defined almost surely with respect to the infinite Bessel point process, of the space of configurations into the space of finite measures on the half-line. The main results of the second part are sufficient conditions for tightness of families of determinantal measures, for convergence of sequences of induced proceses, as well as for sequences of finite-dimensional perturbations of determinantal processes.

arXiv comment20 pages. This is the second paper in the series of three stemming from the preprint arXiv:1312.3161

References in corpus (10)

• Determinantal Processes and Independence
• Determinantal random point fields
• Level-Spacing Distributions and the Bessel Kernel
• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Infinite random matrices and ergodic measures
• Uncertainty principles for integral operators
• Strong annihilating pairs for the Fourier-Bessel transform
• Asymptotic Harmonic Analysis on the Space of Square Complex Matrices
• Ergodic Decomposition for Measures Quasi-Invariant Under Borel Actions of Inductively Compact Groups
• The Classical Hankel Transform In The Kirillov Model

Cited by in corpus (2)

• Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices
• The Ergodic Decomposition of Infinite Pickrell Measures III. The infinite Bessel process as the limit of radial parts of finite-dimensional projections of infinite Pickrell measures