Explicit estimates in the Bramson-Kalikow model

Christophe Gallesco; Sandro Gallo; Daniel Yasumasa Takahashi

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arXiv · 1302.1267

Explicit estimates in the Bramson-Kalikow model

Christophe Gallesco·Sandro Gallo·Daniel Yasumasa Takahashi

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Abstract

The aim of the present article is to explicitly compute parameters for which the Bramson-Kalikow model exhibits phase-transition. The main ingredient of the proof is a simple new criterion for non-uniqueness of $g$-measures. We show that the existence of multiple $g$-measures compatible with a function $g$ can be proved by estimating the $\bar{d}$-distances between some suitably chosen Markov chains. The method is optimal for the important class of binary regular attractive functions, which includes the Bramson-Kalikow model.

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Christophe Gallesco, Sandro Gallo, Daniel Yasumasa Takahashi. 2013-02-06. Explicit estimates in the Bramson-Kalikow model. https://arxiv.org/abs/1302.1267

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