The speed of biased random walk on percolation clusters

Abstract.

 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

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Keywords

  • Random Walk
  • Percolation Cluster
  • Speed Regime
  • Speed Zero
  • Supercritical Percolation