Quenched large deviations in renewal theory (Q6596213)

The aim of this study is to develop \textit{large deviation principles} for \textit{renewal-reward processes in random environments}. In the studied class of models, identified as generalized \textit{pinning models} with general rewards, the authors assume that each renewal involves a reward taking a value in a real separable Banach space. In contrast to the random walks in random environments and random potentials with bounded increments, which are typically analyzed in the literature, renewal times with possibly unbounded and heavy-tailed increments are here considered. Under some specific assumptions (involving the waiting-time distribution, the potential and the reward probability measures), the quenched fluctuations of the total reward over time are characterized. \par The main theoretical results of this study are applied to the following three examples: compound Poisson processes in random environments, pinning of polymers at interfaces with disorder and returns of Markov chains in dynamic random enviroments.