For simple random walk on infinite clusters of Bernoulli bond percolation on Cayley graphs of hyperbolic groups, we prove that the drift and asymptotic entropy depend continuously on the percolation parameter throughout the supercritical phase. Together with the dimension formula, this implies continuity of the Hausdorff dimension of harmonic measure on the Gromov boundary.
We prove locality of the critical probability for Bernoulli site percolation on infinite, connected, locally finite, vertex-transitive graphs, under the usual assumption that the critical probabilities stay uniformly below one. The proof develops site-percolation forms of the two-ghost inequality, sharp-threshold and s...
For Bernoulli bond percolation on every regular tree of degree at least three, we prove that infinite clusters appear strictly before absolutely continuous spectrum. Throughout an explicit supercritical interval, the adjacency operator of every open cluster almost surely has no absolutely continuous component. Together...
We obtain a uniform lower bound for the drift of random walks on hyperbolic spaces in terms of joint minimal displacement. Our main theorem applies to weakly acylindrical actions on Gromov-hyperbolic spaces and is quantitative in all relevant constants. For discrete isometry groups of Hadamard manifolds with pinched ne...
We prove uniform endpoint estimates, killed local limits, and conditioned-bridge invariance principles for triangular arrays of centered, aperiodic, integer-valued random walks with uni- form exponential tails. The endpoint estimates cover all nonnegative heights, while the local limits treat positive diffusive and zer...
In this article, we announce several new results in the ergodic theory of geodesic flows over uniform visibility manifolds without conjugate points. The topics include the ergodicity with respect to the Liouville measure, uniqueness and Bernoulli properties of the measure of maximal entropy and equilibrium states, coun...
Wei-Sheng Wu· Mathematics Research Reports· 0 citations
In this paper we affirmatively resolve the singularity conjecture for finitely supported non-degenerate random walks on cocompact Fuchsian groups. The method we use is based on constructing a pair of geodesic currents, one for the Lebesgue measure and one for the random walk measure, and checking that they are differen...
P. Kosenko, Giulio Tiozzo· 1 citation· ⚡1
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