Quenched large deviations in renewal theory

In this paper we introduce and study renewal–reward processes in random environments where each renewal involves a reward taking values in a Banach space. We derive quenched large deviation principles and identify the associated rate functions in terms of variational formulas involving correctors. W...

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Bibliographic Details
Published in:Stochastic processes and their applications 2024-09, Vol.175, p.104414, Article 104414
Main Authors: den Hollander, Frank, Zamparo, Marco
Format: Article
Language:English
Subjects:
Compound Poisson processes
Pinned polymers
Quenched large deviations
Random environments
Rate functions
Renewal–reward processes
Returns of Markov chains
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Summary:In this paper we introduce and study renewal–reward processes in random environments where each renewal involves a reward taking values in a Banach space. We derive quenched large deviation principles and identify the associated rate functions in terms of variational formulas involving correctors. We illustrate the theory with three examples: compound Poisson processes in random environments, pinning of polymers at interfaces with disorder, and returns of Markov chains in dynamic random environments.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2024.104414