Corpus ID: 236318577

Algebraic area enumeration of random walks on the honeycomb lattice

@inproceedings{Gan2021AlgebraicAE,
  title={Algebraic area enumeration of random walks on the honeycomb lattice},
  author={Li Gan and St'ephane Ouvry and Alexios P. Polychronakos},
  year={2021}
}
We study the enumeration of closed walks of given length and algebraic area on the honeycomb lattice. Using an irreducible operator realization of honeycomb lattice moves, we map the problem to a Hofstadter-like Hamiltonian and show that the generating function of closed walks maps to the grand partition function of a system of particles with exclusion statistics of order g = 2 and an appropriate spectrum, along the lines of a connection previously established by two of the authors… Expand
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