A combinatorial result with applications to self-interacting random walks. (English) Zbl 1232.60055
Summary: We give a series of combinatorial results that can be obtained from any two collections (both indexed by \(\mathbb Z\times \mathbb N\)) of left and right pointing arrows that satisfy some natural relationship. When applied to certain self-interacting random walk couplings, these allow us to reprove some known transience and recurrence results for some simple models. We also obtain new results for one-dimensional multi-excited random walks and for random walks in random environments in all dimensions.
MSC:
| 60K37 | Processes in random environments |
| 05A99 | Enumerative combinatorics |
| 05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
References:
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