Gibbs states on the symbolic space over an infinite alphabet
- Cite this article as:
- Mauldin, R.D. & Urbański, M. Isr. J. Math. (2001) 125: 93. doi:10.1007/BF02773377
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We consider subshifts of finite type on the symbolic space generated by incidence matrices over a countably infinite alphabet. We extend the definition of topological pressure to this context and, as our main result, we construct a new class of Gibbs states of Hölder continuous potentials on these symbol spaces. We establish some basic stochastic properties of these Gibbs states: exponential decay of correlations, central limit theorem and an a.s. invariance principle. This is accomplished via detailed studies of the associated Perron-Frobenius operator and its conjugate operator.