Journal
PHYSICAL REVIEW E
Volume 102, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.102.012154
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Funding
- London Mathematical Laboratory
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We analyze large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q(t) of the time-averaged quantity. First we consider the elephant random walk and a Gaussian variant of this model, identifying two mechanisms for unusual fluctuation behavior, which differ from the Markovian case. In particular, the memory can lead to large-deviation principles with reduced speeds and to nonanalytic rate functions. We then explain how the mechanisms operating in these two models are generic for memory-dependent dynamics and show other examples including a non-Markovian simple exclusion process.
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