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R-positivity and existence of zero-temperature limits of Gibbs measures on nearest neighbors matrices – CORRIGENDUM

Published online by Cambridge University Press:  07 March 2024

Jorge Littin Curinao  and
Gerardo Corredor Rincón
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Abstract

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Type
Corrigendum
Information
Journal of Applied Probability , Volume 61 , Issue 2 , June 2024 , pp. 739
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

The above article was published with an imprecise reference for Ferrari and Martinez [1] (numbered originally as [8] in the article). The correct reference is the subsequent work from 1998 of Ferrari and Martínez [2], entitled Hamiltonians on random walk trajectories and published on Stochastic Processes and their Applications.

The authors would also like to point out that the previous work of Ferrari and Martínez (1993) introduces a continuous fraction approach on chain sequences to study the existence of quasi stationary distributions, which is also relevant, but the notion of Hamiltonians on random walk trajectories was introduced in their subsequent work from 1998.

The updated references are shown below.

References

Ferrari, P. and Martínez, S. (1993). Quasi-stationary distributions: Continued fraction and chain sequence criteria for recurrence. Resenhas do Instituto de Matemática e Estatística da Universidade de São Paulo 1, 321–333.Google Scholar
Ferrari, P. and Martínez, S. (1998). Hamiltonians on random walk trajectories. Stochastic Processes And Their Applications 78-1, 47–68. https://www.sciencedirect.com/science/article/pii/S0304414998000520.CrossRefGoogle Scholar
Curinao, J. and Rincón, G. (2023). R-positivity and the existence of zero-temperature limits of Gibbs measures on nearest-neighbor matrices. Journal of Applied Probability 1–20.Google Scholar