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Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment

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Rassoul-Agha, Firas
Seppalainen, Timo

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We consider random walk with bounded jumps on a hypercubic lattice of arbitrary dimension in a dynamic random environment. The environment is temporally independent and spatially translation invariant. We study the rate functions of the level-3 averaged and quenched large deviation principles from the point of view of the particle. In the averaged case the rate function is a specific relative entropy, while in the quenched case it is a Donsker-Varadhan type relative entropy for Markov processes. We relate these entropies to each other and seek to identify the minimizers of the level-3 to level-1 contractions in both settings. Motivation for this work comes from variational descriptions of the quenched free energy of directed polymer models where the same Markov process entropy appears.

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University of Washington Press

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Mathematics

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Electronic Journal of Probability

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10.1214/17-EJP74

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