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On the Monotonicity of the Speed of Random Walks on a Percolation Cluster of Trees 被引量:1

On the Monotonicity of the Speed of Random Walks on a Percolation Cluster of Trees
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摘要 The authors consider the simple random walk on the infinite cluster of the Bernoulli bond percolation of trees, and investigate the relation between the speed of the simple random walk and the retaining probability p by studying three classes of trees. A sufficient condition is established for Galton-Watson trees. The authors consider the simple random walk on the infinite cluster of the Bernoulli bond percolation of trees, and investigate the relation between the speed of the simple random walk and the retaining probability p by studying three classes of trees. A sufficient condition is established for Galton-Watson trees.
机构地区 LMAM
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第11期1949-1954,共6页 数学学报(英文版)
基金 Supported in part by Grant G1999075106 from the Ministry of Science and Technology of China
关键词 random walk PERCOLATION SPEED MONOTONICITY TREE random walk, percolation, speed, monotonicity, tree
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参考文献6

  • 1Lyons, R., Pemantle, R., Peres, Y.: Ergodic theory on Galton-Watson trees: speed of random walk and dimension of harmonic measure. Ergodic Theory Dynamical Systems, 15, 593 619 (1995)
  • 2Grimmett, G. R., Kesten, H., Zhang, Y.: Random walk on the infinite cluster of the percolation model. Probab. Th. Rel. Fields, 96, 33-44 (1993)
  • 3Benjamini, I., Lyons, R., Schramm, O.: Percolation Perturbations in Potential Theory and Random Walks, in Random Walks and Discrete Potential Theory, Cambridge Univ. Press, 56-84, 1999
  • 4Virag, B.: Anchored expansion and random walk. Geom. Func. Anal., 10, 1588-1605 (2000)
  • 5Chen, D., Peres, Y.: Anchored expansion, percolation and speed, (with an appendix by Gaber Pete). Ann. of Probab., 32, 2978-2995 (2004)
  • 6Lyons, R.: Random walks, capacity, and percolation on trees. Ann. Probab., 20, 2043-2088 (1992)

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