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arXiv · 2304.05996

$\overline{d}$-continuity for countable state shifts

Jasmine Bhullar
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Abstract

For full shifts on finite alphabets, Coelho and Quas showed that the map that sends a H\"older continuous potential $\phi$ to its equilibrium state $\mu_\phi$ is $\overline{d}$-continuous. We extend this result to the setting of full shifts on countable (infinite) alphabets. As part of the proof, we show that the map that sends a strongly positive recurrent potential to its normalization is continuous for potentials on mixing countable state Markov shifts.

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Jasmine Bhullar. 2023-04-12. $\overline{d}$-continuity for countable state shifts. https://doi.org/10.1017/etds.2025.10241

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