---
res:
bibo_abstract:
- The convex set M-a of quasi-invariant measures on a locally convex space E with
given ''shift''-Radon-Nikodym derivatives (i.e., cocycles) a = (a(tk))(k is an
element of K0.tR) is analyzed. The extreme points of M-a are
characterized and proved to be non-empty. A specification (of lattice type) is
constructed so that M-a coincides with the set of the corresponding Gibbs states.
As a consequence, via a well known method due to Dynkin and Follmer a unique representation
of an arbitrary element in M-a in terms of extreme ones is derived. Furthermore,
the corresponding classical Dirichlet forms (E-v, D(E-v)) and their associated
semigroups (T-t(v))(t>0) on L-2(E; v) are discussed. Under a mild positivity condition
it is shown that v is an element of M-a is extreme if and only if (E-v, D(E-v))
is irreducible or equivalently, (T-t(v))(t>0) is ergodic. This implies time-ergodicity
of associated diffusions. Applications to Gibbs states of classical and quantum
lattice models as well as those occuring in Euclidean quantum field theory are
presented. In particular, it is proved that the stochastic quantization of a Guerra-Rosen-Simon
Gibbs state on D-1(R-2) in infinite volume with polynomial interaction is ergodic
if the Gibbs state is extreme (i.e., is a pure phase), which solves a long-standing
open problem. (C) 1997 Academic Press.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Sergio
foaf_name: Albeverio, Sergio
foaf_surname: Albeverio
- foaf_Person:
foaf_givenName: Yuri
foaf_name: Kondratiev, Yuri
foaf_surname: Kondratiev
foaf_workInfoHomepage: http://www.librecat.org/personId=15419
- foaf_Person:
foaf_givenName: Michael
foaf_name: Röckner, Michael
foaf_surname: Röckner
foaf_workInfoHomepage: http://www.librecat.org/personId=10585
bibo_doi: 10.1006/jfan.1997.3099
bibo_issue: '2'
bibo_volume: 149
dct_date: 1997^xs_gYear
dct_identifier:
- UT:A1997XZ22100005
dct_isPartOf:
- http://id.crossref.org/issn/0022-1236
dct_language: eng
dct_publisher: ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS@
dct_subject:
- quasi-invariant measures
- Gibbs states
- irreducibility of
- extremality
- Dirichlet forms
- processes/diffusions
- ergodicity of operator semigroups and of Markov
- ergodicity of measures wrt shifts
- classical and
- quantum lattice models
- Euclidean quantum field theory
dct_title: Ergodicity for the stochastic dynamics of quasi-invariant measures with
applications to Gibbs states@
...