Stochastic adding machines based on Bratteli diagrams

Caprio, Danilo A.; Messaoudi, Ali; Valle, Glauco

doi:10.5802/aif.3364

Stochastic adding machines based on Bratteli diagrams
[Odomètres stochastiques associées aux diagrammes de Bratteli]

Caprio, Danilo A.¹ ; Messaoudi, Ali ¹ ; Valle, Glauco ²

¹ Universidade Estadual Paulista Departamento de Matemática do Instituto de Biociências, Letras e Ciências Exatas Rua Cristóvão Colombo, 2265, Jardim Nazareth, 15054-000 São José do Rio Preto, SP (Brasil)
² Universidade Federal do Rio de Janeiro Instituto de Matemática Caixa Postal 68530, cep 21945-970, Rio de Janeiro (Brasil)

Annales de l'Institut Fourier, Tome 70 (2020) no. 6, pp. 2543-2581.

Résumé
Abstract

Dans cet article, nous définissons des chaînes de Markov associées aux applications de Vershik sur des diagrammes de Bratteli. Nous étudions des propriétés probabilistes et spectrales de leurs opérateurs de transition et nous prouvons que les spectres de ces opérateurs sont liés à des ensembles de Julia de dimensions supérieures. Nous étudions également des propriétés topologiques de ces spectres.

In this paper, we define some Markov chains associated with Vershik maps on Bratteli diagrams. We study probabilistic and spectral properties of their transition operators and we prove that the spectra of these operators are connected to Julia sets in higher dimensions. We also study topological properties of these spectra.

Reçu le : 2018-01-30
Révisé le : 2019-04-15
Accepté le : 2019-12-20
Publié le : 2021-04-15

DOI : 10.5802/aif.3364

Classification : 37A30, 37F50, 60J10, 47A10
Keywords: Markov chains, stochastic Vershik map, Bratteli diagrams, spectrum of transition operators, fibered Julia sets
Mot clés : chaînes de Markov, application de Vershik stochastique, diagrammes de Bratteli, spectre des opérateurs de transition, ensembles de Julia fibrés

Affiliations des auteurs :

Caprio, Danilo A. ¹ ; Messaoudi, Ali ¹ ; Valle, Glauco ²

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     title = {Stochastic adding machines based on {Bratteli} diagrams},
     journal = {Annales de l'Institut Fourier},
     pages = {2543--2581},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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     year = {2020},
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Caprio, Danilo A.; Messaoudi, Ali; Valle, Glauco. Stochastic adding machines based on Bratteli diagrams. Annales de l'Institut Fourier, Tome 70 (2020) no. 6, pp. 2543-2581. doi : 10.5802/aif.3364. http://www.numdam.org/articles/10.5802/aif.3364/

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