We consider biased random walk on supercritical percolation clusters in ℤ2. We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive.
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Received: 20 November 2002 / Revised version: 17 January 2003 Published online: 15 April 2003
Research supported by Microsoft Research graduate fellowship.
Research partially supported by the DFG under grant SPP 1033.
Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley.
Mathematics Subject Classification (2000): 60K37; 60K35; 60G50
Key words or phrases: Percolation – Random walk
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Berger, N., Gantert, N. & Peres, Y. The speed of biased random walk on percolation clusters. Probab. Theory Relat. Fields 126, 221–242 (2003). https://doi.org/10.1007/s00440-003-0258-2
- Random Walk
- Percolation Cluster
- Speed Regime
- Speed Zero
- Supercritical Percolation