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Geodesics and Recurrence of Random Walks in Disordered Systems

   
@article{ECP1052,
	author = {Daniel Boivin and Jean-Marc Derrien},
	title = {Geodesics and Recurrence of Random Walks in Disordered Systems},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {7},
	year = {2002},
	keywords = {Random environment with stationary conductances;Geodesics in first-passage percolation model; Reversible random walks on\$Z^2\$;Recurrence and transience.},
	abstract = {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, ergodic and have a finite moment of order $\alpha > 1/2$, then the number of geodesics is either $0$ or $+\infty$. We construct a model with stationary passage times such that $E\lbrack t(e)^\alpha\rbrack  < \infty$, for every $0 < \alpha < 1/2$,  and with a unique geodesic.  The recurrence/transience properties of reversible random walks  in a random environment with  stationary  conductances $( a(e);e$ is an edge of $\mathbb{Z}^2)$  are considered.},
	pages = {no. 11, 101-115},
	issn = {1083-589X},
	doi = {10.1214/ECP.v7-1052},    
        url = {http://ecp.ejpecp.org/article/view/1052}}