Derives stationary measures for zero-temperature random polymer models via reductions to two bijections with independence preservation, noting degeneracy explains atoms and yields links between models including new ones for the river delta model.
A Large deviation principle for last passage times in an asymmetric Bernoulli potential
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abstract
We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we compute explicit limiting logarithmic moment generating functions for both the classical and the invariant models. The shape function of this model exhibits a flat edge in certain directions, and we also discuss the rate function and limiting log-moment generating functions in those directions.
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math.PR 1years
2021 1verdicts
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On the stationary solutions of random polymer models and their zero-temperature limits
Derives stationary measures for zero-temperature random polymer models via reductions to two bijections with independence preservation, noting degeneracy explains atoms and yields links between models including new ones for the river delta model.