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### Non-uniqueness for specifications in $\ell^{2+\epsilon}$

**Mathematical Physics & Probability**

Speaker: | Noam Berger, Caltech |

Location: | 693 Kerr |

Start time: | Tue, Oct 19 2004, 3:10PM |

Keane, Berbee and others have studied the question of which specifications (aka $g$-functions) admit unique Gibbs measure. Bramson and Kalikow contructed the first example of a regular and continuous specification which admits multiple measures. For every $p>2$, we contruct a regular and continuous specification, whose variation is in $\ell^p$, that admits multiple Gibbs measures. This shows that a recent condition of Oberg and Johansson is tight. Based on joint work with Christopher Hoffman and Vlada Sidoravicius.