When random walks on a square lattice are biased horizontally to move solely
to the right, the probability distribution of their algebraic area can be
exactly obtained. We explicitly map this biased classical random system on a
non hermitian Hofstadter-like quantum model where a charged particle on a
square lattice coupled to a perpendicular magnetic field hopps only to the
right. In the commensurate case when the magnetic flux per unit cell is
rational, an exact solution of the quantum model is obtained. Periodicity on
the lattice allows to relate traces of the Nth power of the Hamiltonian to
probability distribution generating functions of biased walks of length N.Comment: 14 pages, 7 figure