An example of non-unique g-measures

PAUL HULSE

doi:10.1017/S0143385705000489

Abstract

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An example of non-unique g-measures is constructed. The function g satisfies a certain summability condition, thereby providing a counterexample to the claim in an earlier paper that all such g have a unique g-measure.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

JOHANSSON, ANDERS and ÖBERG, ANDERS 2008. Square summability of variations and convergence of the transfer operator. Ergodic Theory and Dynamical Systems, Vol. 28, Issue. 4, p. 1145.

De Santis, Emilio and Piccioni, Mauro 2013. Perfect Simulation of Autoregressive Models with Infinite Memory. Journal of Statistical Physics, Vol. 150, Issue. 6, p. 1017.

C, Gallesco S, Gallo and Y, Takahashi D 2014. Explicit estimates in the Bramson–Kalikow model. Nonlinearity, Vol. 27, Issue. 9, p. 2281.

GALLO, SANDRO and TAKAHASHI, DANIEL Y. 2014. Attractive regular stochastic chains: perfect simulation and phase transition. Ergodic Theory and Dynamical Systems, Vol. 34, Issue. 5, p. 1567.

Trejo-Valencia, Liliana and Ugalde, Edgardo 2015. Projective distance and $g$-measures. Discrete and Continuous Dynamical Systems - B, Vol. 20, Issue. 10, p. 3565.

Bushaw, Neal Gunderson, Karen and Kalikow, Steven 2016. Random Markov processes for countable and uncountable alphabets. Israel Journal of Mathematics, Vol. 216, Issue. 1, p. 181.

Dias, J. C. A. and Friedli, S. 2016. Uniqueness vs. non-uniqueness for complete connections with modified majority rules. Probability Theory and Related Fields, Vol. 164, Issue. 3-4, p. 893.

Gallesco, Christophe Gallo, Sandro and Takahashi, Daniel Y. 2018. Dynamic uniqueness for stochastic chains with unbounded memory. Stochastic Processes and their Applications, Vol. 128, Issue. 2, p. 689.

BERGER, NOAM HOFFMAN, CHRISTOPHER and SIDORAVICIUS, VLADAS 2018. Non-uniqueness for specifications in . Ergodic Theory and Dynamical Systems, Vol. 38, Issue. 4, p. 1342.

Bissacot, Rodrigo Endo, Eric O. van Enter, Aernout C. D. and Le Ny, Arnaud 2018. Entropic Repulsion and Lack of the g-Measure Property for Dyson Models. Communications in Mathematical Physics, Vol. 363, Issue. 3, p. 767.

BERGHOUT, STEVEN FERNÁNDEZ, ROBERTO and VERBITSKIY, EVGENY 2019. On the relation between Gibbs and -measures. Ergodic Theory and Dynamical Systems, Vol. 39, Issue. 12, p. 3224.

Cioletti, L. and Lopes, A. O. 2019. Correlation inequalities and monotonicity properties of the Ruelle operator. Stochastics and Dynamics, Vol. 19, Issue. 06, p. 1950048.

Chazottes, Jean-René Gallo, Sandro and Takahashi, Daniel Y. 2023. Gaussian concentration bounds for stochastic chains of unbounded memory. The Annals of Applied Probability, Vol. 33, Issue. 5,

Cuneo, Noé and Raquépas, Renaud 2024. Large Deviations of Return Times and Related Entropy Estimators on Shift Spaces. Communications in Mathematical Physics, Vol. 405, Issue. 6,

Berger, Noam Conache, Diana Johansson, Anders and Öberg, Anders 2025. Uniqueness and mixing properties of Doeblin measures. Probability Theory and Related Fields, Vol. 193, Issue. 3-4, p. 1161.

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An example of non-unique g-measures

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

An example of non-unique g-measures

Abstract

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