Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms

DOI10.1215/kjm/1250518934zbMath0874.57028OpenAlexW1529114128MaRDI QIDQ1842783

Hiroaki Shimomura

Publication date: 3 November 1997

Published in: Journal of Mathematics of Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/kjm/1250518934

zbMATH Keywords

configuration spaceergodicityPoisson measureBorel measure\(C^ \infty\)-manifoldmeasurable subsets

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Differential topological aspects of diffeomorphisms (57R50) Measures (Gaussian, cylindrical, etc.) on manifolds of maps (58D20)

Related Items (9)

Topological transformation groups of manifolds over non-Archimedean fields, their representations, and quasi-invariant measures. I. ⋮ Unitary representations of the group of diffeomorphisms via restricted product measures with infinite mass. II ⋮ A biorthogonal approach to the infinite dimensional fractional Poisson measure ⋮ Poincaré and weak Poincaré inequalities for the mixed Poisson measure ⋮ Dirichlet forms and diffusion processes for fermion random point fields ⋮ Quasi-invariant measures on the group of diffeomorphisms and smooth vectors of unitary representations ⋮ Poisson cluster measures: Quasi-invariance, integration by parts and equilibrium stochastic dynamics ⋮ Analysis and geometry on configuration spaces ⋮ Generic non-singular Poisson suspension is of type III₁

This page was built for publication: Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms