Department of Mathematics2024-11-0920171083-648910.1214/17-EJP742-s2.0-85023595137https://hdl.handle.net/20.500.14288/1791We 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.pdfMathematicsJournal Articlehttps://doi.org/10.1214/17-EJP74404789400002Q3NOIR01461