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Velocity surface disorder of large deviation rate functions of the random walk in strongly mixing environment
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In this work, we establish the existence of large deviation principles of random walk in strongly mixing environments. The quenched and annealed rate functions have the same zero set whose shape is either a singleton point or a line segment, with an illustrative example communicated and given by F. Rassoul-Agha. Whenever the level of disorder is controlled, the two rate functions are shown to conform on compact sets at the boundary and in the interior both under strongly mixing conditions.
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Non-conformality of large deviations of moving average of the random walk in strongly mixing environment
For any positive disorder in a strongly mixing random environment, quenched and annealed large deviation rate functions for the random walk disagree at some interior velocity.
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