Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems
3 July 2023
Develops quenched thermodynamic formalism for open random interval maps with holes
Proves existence and uniqueness of random conformal and invariant measures
Shows exponential decay of correlations for invariant measure
Relates escape rate to difference in expected pressures
Obtains Hausdorff dimension of survivor set from expected pressure
Proves abstract perturbation formula for leading Lyapunov multipliers
Applies perturbation theory to obtain quenched extreme value theory
Proves quenched statistical limit theorems for equilibrium states
A more literal title describing the main contributions
The paper develops a framework for open random dynamical systems generated by interval maps with holes that terminate trajectories. Key results include proving existence and uniqueness of random conformal and invariant measures, exponential decay of correlations, relating the escape rate to pressures, and obtaining the Hausdorff dimension of the survivor set. The second part of the paper proves an abstract perturbation formula for leading Lyapunov multipliers of operator cocycles and applies it to obtain a quenched extreme value theory and statistical limit theorems.
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