期刊
PROBABILITY THEORY AND RELATED FIELDS
卷 167, 期 3-4, 页码 1057-1116出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-016-0699-z
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资金
- Laboratoire de Probabilites et Modeles Aleatoires UMR CNRS [7599]
- Universite Paris-Diderot-Paris 7
- Packard Foundation through I.C.'s Packard Fellowship
- NSF [DMS-1208998]
- Clay Mathematics Institute through a Clay Research Fellowship
- Institute Henri Poincare through the Poincare Chair
- Packard Foundation through a Packard Fellowship for Science and Engineering
We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in which performs nearest neighbour jumps with transition probabilities drawn according to the Beta distribution. We also describe a related directed polymer model, which is a limit of the q-Hahn interacting particle system. Using a Fredholm determinant representation for the quenched probability distribution function of the walker's position, we are able to prove second order cube-root scale corrections to the large deviation principle satisfied by the walker's position, with convergence to the Tracy-Widom distribution. We also show that this limit theorem can be interpreted in terms of the maximum of strongly correlated random variables: the positions of independent walkers in the same environment. The zero-temperature counterpart of the Beta RWRE can be studied in a parallel way. We also prove a Tracy-Widom limit theorem for this model.
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