Infinite determinantal measures and the ergodic decomposition of infinite
Izvestiya. Mathematics , Tome 80 (2016) no. 2, pp. 299-315
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The second paper in this series is devoted to the convergence of sequences
of infinite determinantal measures, understood as the convergence
of sequences of the corresponding finite determinantal measures. Besides the
weak topology in the space of probability measures on the space
of configurations, we also consider the natural immersion (defined almost
surely with respect to the infinite Bessel process) of the space
of configurations into the space of finite measures on the half-line, which
induces a weak topology in the space of finite measures on the space of finite
measures on the half-line. The main results of the present paper are sufficient
conditions for the tightness of families and the convergence of sequences
of induced determinantal processes as well as for the convergence of processes
corresponding to finite-rank perturbations of operators.
Keywords:
determinantal processes, infinite determinantal measures, ergodic decomposition,
infinite-dimensional harmonic analysis, infinite unitary group, scaling limits,
Jacobi polynomials, Harish-Chandra–Itzykson–Zuber orbit integral.
@article{IM2_2016_80_2_a1,
author = {A. I. Bufetov},
title = {Infinite determinantal measures and the ergodic decomposition of infinite},
journal = {Izvestiya. Mathematics },
pages = {299--315},
publisher = {mathdoc},
volume = {80},
number = {2},
year = {2016},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_2_a1/}
}
A. I. Bufetov. Infinite determinantal measures and the ergodic decomposition of infinite. Izvestiya. Mathematics , Tome 80 (2016) no. 2, pp. 299-315. http://geodesic.mathdoc.fr/item/IM2_2016_80_2_a1/