Aperiodicity of cocycles and conditional local limit theorems

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Operator renewal theory and mixing rates for dynamical systems with infinite measure (2010, background): “(It should be noted that in our setting, the proof in [5] is greatly simplified since in [5] φ is not assumed to be locally constant and F is not required to satisfy Adler’s condition or finite images.”
Annealed and quenched limit theorems for random expanding dynamical systems (2013, methodology): “See the works of Rousseau-Egele [63], Morita [60], Broise [16] or Aaronson-Denker-Sarig-Zweimuller [2] for one-dimensional deterministic examples.”