Countable Alphabet Random Subhifts of Finite Type with Weakly Positive Transfer Operator.
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| Title: | Countable Alphabet Random Subhifts of Finite Type with Weakly Positive Transfer Operator. |
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| Authors: | Mayer, Volker1 volker.mayer@univ-lille1.fr, Urbański, Mariusz2 urbanski@unt.edu |
| Source: | Journal of Statistical Physics. Sep2015, Vol. 160 Issue 5, p1405-1431. 27p. |
| Subjects: | Transfer operators, Operator theory, Thermodynamics, Markov processes, Central limit theorem |
| Abstract: | We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of big images property and under the absence of uniform positivity of the transfer operator. We first establish the existence of random conformal measures along with good bounds for the iterates of the Perron-Frobenius operator. Then, using the technique of positive cones and proving a version of Bowen's type contraction (see Equilibrium states and the ergodic theory of Anosov diffeomorphisms, ), we also establish a fairly complete thermodynamical formalism. This means that we prove the existence and uniqueness of fiberwise invariant measures (giving rise to a global invariant measure) equivalent to the fiberwise conformal measures. Furthermore, we establish the existence of a spectral gap for the transfer operators, which in the random context precisely means the exponential rate of convergence of the normalized iterated transfer operator. This latter property in a relatively straightforward way entails the exponential decay of correlations and the Central Limit Theorem. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Countable Alphabet Random Subhifts of Finite Type with Weakly Positive Transfer Operator. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mayer%2C+Volker%22">Mayer, Volker</searchLink><relatesTo>1</relatesTo><i> volker.mayer@univ-lille1.fr</i><br /><searchLink fieldCode="AR" term="%22Urbański%2C+Mariusz%22">Urbański, Mariusz</searchLink><relatesTo>2</relatesTo><i> urbanski@unt.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Statistical+Physics%22">Journal of Statistical Physics</searchLink>. Sep2015, Vol. 160 Issue 5, p1405-1431. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Transfer+operators%22">Transfer operators</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+theory%22">Operator theory</searchLink><br /><searchLink fieldCode="DE" term="%22Thermodynamics%22">Thermodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br /><searchLink fieldCode="DE" term="%22Central+limit+theorem%22">Central limit theorem</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of big images property and under the absence of uniform positivity of the transfer operator. We first establish the existence of random conformal measures along with good bounds for the iterates of the Perron-Frobenius operator. Then, using the technique of positive cones and proving a version of Bowen's type contraction (see Equilibrium states and the ergodic theory of Anosov diffeomorphisms, ), we also establish a fairly complete thermodynamical formalism. This means that we prove the existence and uniqueness of fiberwise invariant measures (giving rise to a global invariant measure) equivalent to the fiberwise conformal measures. Furthermore, we establish the existence of a spectral gap for the transfer operators, which in the random context precisely means the exponential rate of convergence of the normalized iterated transfer operator. This latter property in a relatively straightforward way entails the exponential decay of correlations and the Central Limit Theorem. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10955-015-1287-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 1405 Subjects: – SubjectFull: Transfer operators Type: general – SubjectFull: Operator theory Type: general – SubjectFull: Thermodynamics Type: general – SubjectFull: Markov processes Type: general – SubjectFull: Central limit theorem Type: general Titles: – TitleFull: Countable Alphabet Random Subhifts of Finite Type with Weakly Positive Transfer Operator. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mayer, Volker – PersonEntity: Name: NameFull: Urbański, Mariusz IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 00224715 Numbering: – Type: volume Value: 160 – Type: issue Value: 5 Titles: – TitleFull: Journal of Statistical Physics Type: main |
| ResultId | 1 |
