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Doctoral Thesis
DOI
Document
Author
Full name
Elmer Rusbert Calderón Beltrán
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Proença, Rodrigo Bissacot (President)
Freire Junior, Ricardo dos Santos
Senti, Samuel Anton
Silveira, Mariana Rodrigues da
Zhang, Xuan
Title in Portuguese
Medidas DLR e transições de fase tipo volume em shifts de Markov com alfabeto enumerável
Keywords in Portuguese
Medidas conformes
Medidas DLR $\sigma-$finita
shift de Markov
Shift de renewal
Transições de fase tipo volume
Abstract in Portuguese
Introduzimos a extensão natural da definição de medida DLR para medidas sigma-finitas em shift de Markov com alfabeto enumerável. Provamos que o conjunto de medidas DLR contém o conjunto de medidas conformes associadas aos potenciais satisfazendo a condição de Walters. No caso BIP ou quando o potencial normaliza o operador de Ruelle, provamos que as noções de DLR e conformes coincidem. No shift de renewal obtemos uma caracterização de quando as medidas conformes são infinitas, estudamos o problema para descrever os casos em que o conjunto de medidas conformes pula de medidas finitas para infinitas quando consideramos altas e baixas temperaturas, respectivamente.
Title in English
DLR Measures and Volume-Type Phase Transitions in Markov shifts with Enumerable Alphabet
Keywords in English
Conformal measure
DLR measure $\sigma-$finite
Markov shift
Phase transition type volume
Shift of renewal
Abstract in English
We introduce the natural extension of the definition of DLR measure for sigma-finite measures on countable Markov shifts. We prove that the set of DLR measures contains the set of conformal measures associated to Walters potentials. In the BIP case or when the potential normalizes the Ruelle's operator we prove that the notions of DLR and conformal coincide. On renewal type shifts we obtained a characterization when the conformal measures are infinite, we study the problem to describe the cases when the set of conformal measures jumps from finite to infinite measures when we consider high and low temperatures, respectively.
 
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doutorado.pdf (965.42 Kbytes)
Publishing Date
2019-04-24
 
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