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Percolation on fuchsian groups

Steven P. Lalley — 1998

Annales de l'I.H.P. Probabilités et statistiques

Random walks on co-compact fuchsian groups

Sébastien Gouëzel; Steven P. Lalley — 2013

Annales scientifiques de l'École Normale Supérieure

It is proved that the Green’s function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence $R$ . It is also shown that Ancona’s inequalities extend to $R$ , and therefore that the Martin boundary for $R$ -potentials coincides with the natural geometric boundary $S^{1}$ , and that the Martin kernel is uniformly Hölder continuous. Finally, this implies a local limit theorem for the transition probabilities: in the aperiodic case, $p^{n} (x, y) \sim C_{x, y} R^{- n} n^{- 3 / 2}$ .

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Percolation on fuchsian groups

Random walks on co-compact fuchsian groups

Strict convexity of the limit shape in first-passage percolation.

An oriented competition model on $Z_{+}^{2}$ .

Geometric interpretation of half-plane capacity.

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

Percolation on fuchsian groups

Random walks on co-compact fuchsian groups

Strict convexity of the limit shape in first-passage percolation.

An oriented competition model on Z + 2 .

Geometric interpretation of half-plane capacity.

An oriented competition model on $Z_{+}^{2}$ .