We study a class of stationary processes indexed by
ℤd that are defined via minors of
d-dimensional (multilevel) Toeplitz matrices. We obtain necessary
and sufficient conditions for phase multiplicity (the existence of a
phase transition) analogous to that which occurs in statistical
mechanics. Phase uniqueness is equivalent to the presence of a strong
K-property, a particular strengthening of the usual K (Kolmogorov)
property. We show that all of these processes are Bernoulli shifts
(isomorphic to independent identically distributed (i.i.d.) processes
in the sense of ergodic theory). We obtain estimates of their
entropies, and we relate these processes via stochastic domination to
product measures.
@article{1082137353,
author = {Lyons, Russell and Steif, Jeffrey E.},
title = {Stationary determinantal processes: Phase multiplicity, Bernoullicity, entropy, and domination},
journal = {Duke Math. J.},
volume = {120},
number = {3},
year = {2003},
pages = { 515-575},
language = {en},
url = {http://dml.mathdoc.fr/item/1082137353}
}
Lyons, Russell; Steif, Jeffrey E. Stationary determinantal processes: Phase multiplicity, Bernoullicity, entropy, and domination. Duke Math. J., Tome 120 (2003) no. 3, pp. 515-575. http://gdmltest.u-ga.fr/item/1082137353/