Monotone interaction of walk and graph: recurrence versus transience
  We consider recurrence versus transience for models of random walks on domains of $\mathbb{Z}^d$, in which monotone interaction enforces domain growth as a result of visits by the walk (or probes it sent), to the neighborhood of domain boundary. 
Amir Dembo, Ruojun Huang, Vladas Sidoravicius
math.PR