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\iteman{io-port 06089446}
\itemau{Nazarenko, A.V.}
\itemti{Directed random walk on the lattices of genus two.}
\itemso{Int. J. Mod. Phys. B 25, No. 26, 3415-3433 (2011).}
\itemab
Summary: The object of the present investigation is an ensemble of self-avoiding and directed graphs belonging to eight-branching Cayley tree (Bethe lattice) generated by the Fuchsian group of a Riemann surface of genus two and embedded in the Poincar\'e unit disk. We consider two-parametric lattices and calculate the multifractal scaling exponents for the moments of the graph lengths distribution as functions of these parameters. We show the results of numerical and statistical computations, where the latter are based on a random walk model.
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\itemcc{}
\itemut{directed random walk; Cayley tree}
\itemli{doi:10.1142/S0217979211101831}
\end