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May 2015 A note on the Bramson–Kalikow process
Sacha Friedli
Braz. J. Probab. Stat. 29(2): 427-442 (May 2015). DOI: 10.1214/14-BJPS256

Abstract

We consider discrete-time stationary processes with long-range dependencies, $X_{n}\in\{\pm1\}$, ${n\in\mathbb{Z}}$, specified by a regular attractive $g$-function, similar to those considered by Bramson and Kalikow [Israel J. Math. 84 (1993) 153–160]. We give an explicit set of conditions that imply the existence of at least two distinct processes specified by the same $g$-function, and consider a few examples that emphasize the role played by the smoothness of the majority rule at the origin.

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Sacha Friedli. "A note on the Bramson–Kalikow process." Braz. J. Probab. Stat. 29 (2) 427 - 442, May 2015. https://doi.org/10.1214/14-BJPS256

Information

Published: May 2015
First available in Project Euclid: 15 April 2015

zbMATH: 1321.60071
MathSciNet: MR3336874
Digital Object Identifier: 10.1214/14-BJPS256

Keywords: $g$-function , complete connections , Long-range , majority rule , phase transition

Rights: Copyright © 2015 Brazilian Statistical Association

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Vol.29 • No. 2 • May 2015
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