Page 1

Displaying 1 – 2 of 2

Showing per page

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 ) C x , y R - n n - 3 / 2 .

Currently displaying 1 – 2 of 2

Page 1