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Fixed points of an infinite-dimensional operator related to Gibbs measures.
- Source :
-
Theoretical & Mathematical Physics . Feb2023, Vol. 214 Issue 2, p282-295. 14p. - Publication Year :
- 2023
-
Abstract
- We describe fixed points of an infinite-dimensional nonlinear operator related to a hard-core (HC) model with a countable set of spin values on a Cayley tree. This operator is defined by a countable set of parameters , , . We find a sufficient condition on these parameters under which the operator has a unique fixed point. When this condition is not satisfied, we show that the operator may have up to five fixed points. We also prove that every fixed point generates a normalizable boundary law and therefore defines a Gibbs measure for the given HC model. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONLINEAR operators
*GIBBS sampling
Subjects
Details
- Language :
- English
- ISSN :
- 00405779
- Volume :
- 214
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Theoretical & Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 162181888
- Full Text :
- https://doi.org/10.1134/S0040577923020125