Thermodynamic Formalism for Random Non-uniformly Expanding Maps

Manuel Stadlbauer, Shintaro Suzuki, Paulo Varandas

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every measurable and fibered C1-potential at high temperature admits a unique equilibrium state which satisfies a weak Gibbs property, and has exponential decay of correlations. The arguments combine a functional analytic approach for the decay of correlations (using Birkhoff cone methods) and Carathéodory-type structures to describe the relative pressure of not necessary compact invariant sets in random dynamical systems. We establish also a variational principle for the relative pressure of random dynamical systems.

Original languageEnglish
Pages (from-to)369-427
Number of pages59
JournalCommunications in Mathematical Physics
Issue number1
Publication statusPublished - 2021 Jul

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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