Details

Autor(en) / Beteiligte

• JAERISCH, JOHANNES

Titel

Group-extended Markov systems, amenability, and the Perron-Frobenius operator

Ist Teil von

• Proceedings of the American Mathematical Society, 2015-01, Vol.143 (1), p.289-300

Ort / Verlag

American Mathematical Society

Erscheinungsjahr

2015

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We characterise amenability of a countable group in terms of the spectral radius of the Perron-Frobenius operator associated to a group extension of a countable Markov shift and a Hölder continuous potential. This extends a result of Day for random walks and recent work of Stadlbauer for dynamical systems. Moreover, we show that if the potential satisfies a symmetry condition with respect to the group extension, then the logarithm of the spectral radius of the Perron-Frobenius operator is given by the Gurevič pressure of the potential.