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The speed of biased random walk on percolation clusters
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  • Published: June 2003

The speed of biased random walk on percolation clusters

  • Noam Berger1,
  • Nina Gantert2 &
  • Yuval Peres1 

Probability Theory and Related Fields volume 126, pages 221–242 (2003)Cite this article

  • 283 Accesses

  • 59 Citations

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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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Authors and Affiliations

  1. University of California, Department of Statistics, 367 Evans Hall, CA 94720-3860, USA. e-mail: {noam, peres}@stat.berkeley.edu, , , , , , US

    Noam Berger & Yuval Peres

  2. University of Karlsruhe, Germany. e-mail: n.gantert@math.uni-karlsruhe.de, , , , , , DE

    Nina Gantert

Authors
  1. Noam Berger
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  2. Nina Gantert
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  3. Yuval Peres
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Additional information

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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  • Issue Date: June 2003

  • DOI: https://doi.org/10.1007/s00440-003-0258-2

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Keywords

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