A Thermodynamic Formalism for Continuous Time Markov Chains with Values on the Bernoulli Space: Entropy, Pressure and Large Deviations
| hal.structure.identifier | Instituto de Matémàtica | |
| dc.contributor.author | LOPES, Artur | |
| hal.structure.identifier | Instituto de Matematica [Porto Alegre, RS] [IM/UFRGS] | |
| dc.contributor.author | NEUMANN, Adriana | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | THIEULLEN, Philippe | |
| dc.date.accessioned | 2024-04-04T02:18:41Z | |
| dc.date.available | 2024-04-04T02:18:41Z | |
| dc.date.issued | 2013 | |
| dc.identifier.issn | 0022-4715 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189338 | |
| dc.description.abstractEn | Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice {1, . . . , d}N (also known as the Bernoulli space). Initially, we consider as the infinitesimal generator the operator L = LA − I, where LA is a discrete time Ruelle operator (transfer operator), and A : {1, . . . , d}N →R is a given fixed Lipschitz function. The associated continuous time stationary Markov chain will define the a priori probability. Given a Lipschitz interaction V : {1, . . . , d}N →R, we are interested in Gibbs (equilibrium) state for such V . This will be another continuous time stationary Markov chain. In order to analyze this problem we will use a continuous time Ruelle operator (transfer operator) naturally associated to V . Among other things we will show that a continuous time Perron-Frobenius Theorem is true in the case V is a Lipschitz function. We also introduce an entropy, which is negative (see also Lopes et al. in Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature. Arxiv, 2012), and we consider a variational principle of pressure. Finally, we analyze large deviations properties for the empirical measure in the continuous time setting using results by Y. Kifer (Tamsui Oxf. J. Manag. Sci. 321(2):505- 524, 1990). In the last appendix of the paper we explain why the techniques we develop here have the capability to be applied to the analysis of convergence of a certain version of the Metropolis algorithm. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.title.en | A Thermodynamic Formalism for Continuous Time Markov Chains with Values on the Bernoulli Space: Entropy, Pressure and Large Deviations | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s10955-013-0796-7 | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.identifier.arxiv | 1307.0237 | |
| bordeaux.journal | Journal of Statistical Physics | |
| bordeaux.page | 894 - 933 | |
| bordeaux.volume | 152 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00963869 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00963869v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Statistical%20Physics&rft.date=2013&rft.volume=152&rft.issue=5&rft.spage=894%20-%20933&rft.epage=894%20-%20933&rft.eissn=0022-4715&rft.issn=0022-4715&rft.au=LOPES,%20Artur&NEUMANN,%20Adriana&THIEULLEN,%20Philippe&rft.genre=article |
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