On the speed of distance-stationary sequences. (English) Zbl 1469.60314
Summary: We prove a formula for the speed of distance-stationary random sequences generalizing the law of large numbers of Karlsson and Ledrappier. A particular case is the classical formula for the largest Lyapunov exponent of i.i.d. matrix products, but our result has applications in various different contexts. In many situations it gives a method to estimate the speed, and in others it allows to obtain results of dimension drop for escape measures related to random walks. We show applications to stationary reversible random trees with conductances, Bernoulli bond percolation of Cayley graphs, and random walks on cocompact Fuchsian groups.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 05C80 | Random graphs (graph-theoretic aspects) |
| 60G50 | Sums of independent random variables; random walks |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
| 60K37 | Processes in random environments |
| 05C81 | Random walks on graphs |
Keywords:
random walk speed; random trees; Bernoulli percolation; harmonic measure; cocompact Fuchsian groupsReferences:
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