Random-walk in Beta-distributed random environment

@article{Barraquand2015RandomwalkIB,
  title={Random-walk in Beta-distributed random environment},
  author={Guillaume Barraquand and Ivan Corwin},
  journal={Probability Theory and Related Fields},
  year={2015},
  volume={167},
  pages={1057-1116}
}
We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in $$\mathbb {Z}$$Z 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… 
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