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On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks
Probabilities Wienertest Paley-Zygmund inequality
2009/5/4
We consider a continuous time random walk on the d-dimensional lattice Zd: the jump rates are time dependent, but symmetric and strongly elliptic with ellipticity constants independent of time. We inv...
A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment
random walk in random environment RWRE law of large numbers
2009/4/29
We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general...
Geodesics and Recurrence of Random Walks in Disordered Systems
Random environment with stationary conductances Geodesicsin in first-passage percolation model Recurrence and transience
2009/4/29
In a first-passage percolation model on the square lattice $Z^2$, if the passage times are independent then the number of geodesics is either $0$ or $+infty$. If the passage times are stationary, ergo...
Recurrent Graphs where Two Independent Random Walks Collide Finitely Often
Random walk Comb lattice collisions
2009/4/28
We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from $Z^2$ by rem...