A combinatorial result with applications to self-interacting random walks

作者：Holmes Mark^*; Sali**ury Thomas S

来源：Journal of Combinatorial Theory - Series A, 2012, 119(2): 460-475.

DOI：10.1016/j.jcta.2011.10.004

• Random walk
• Coupling
• Monotonicity

We give a series of combinatorial results that can be obtained from any two collections (both indexed by Z x 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.

• 出版日期2012-2