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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.