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Some remarks on random zeta functions

Published online by Cambridge University Press:  06 August 2002

JÉRÔME BUZZI
JÉRÔME BUZZI
Affiliation:
Centre de Mathématiques de l'Ecole Polytechnique, U.M.R. 7640 du C.N.R.S., 91128 Palaiseau, France (e-mail: [email protected])
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Abstract

We answer in the negative a question of Viviane Baladi: in contrast to its deterministic or averaged versions, the random zeta function has no meromorphic extensions, hence no poles which would describe the Lyapunov exponents of the corresponding random transfer operator. In fact we show that the sequence of traces of the random iterates of this operator does not determine almost surely these exponents.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 4 , August 2002 , pp. 1031 - 1040
Copyright
© 2002 Cambridge University Press

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