Hamiltonian and exclusion statistics approach to discrete forward-moving paths.

@article{Ouvry2021HamiltonianAE,
  title={Hamiltonian and exclusion statistics approach to discrete forward-moving paths.},
  author={S. Ouvry and A. Polychronakos},
  journal={Physical review. E},
  year={2021},
  volume={104 1-1},
  pages={
          014143
        }
}
We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for paths with arbitrary starting and ending points, expressing it as a rational combination of determinants. Exploiting a connection between random walks and quantum exclusion statistics that we previously established, we express this generating function in… Expand

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