Abstract
In this paper, we consider three different exponential rates of growth associated to a symmetric random walk on a countable group: the spectral gap, the entropy and the decay of the fundamental state along the paths of the random walk. We prove general inequalities between these numbers. We hope that these inequalities, and the characterization of the cases of equality, would enable us to express fine properties of the group through rather coarse invariants.
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References
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© 1992 Springer Science+Business Media New York
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Ledrappier, F. (1992). Sharp Estimates for the Entropy. In: Picardello, M.A. (eds) Harmonic Analysis and Discrete Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2323-3_23
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DOI: https://doi.org/10.1007/978-1-4899-2323-3_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-2325-7
Online ISBN: 978-1-4899-2323-3
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