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A monotonicity property for random walk in a partially random environment

Author

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  • Holmes, Mark
  • Sun, Rongfeng

Abstract

We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Zd that is an extension of a result of Bolthausen et al. (2003) [4]. We use this result, along with the lace expansion for self-interacting random walks, to prove a monotonicity result for the first coordinate of the speed of the random walk under some strong assumptions on the distribution of the environment.

Suggested Citation

  • Holmes, Mark & Sun, Rongfeng, 2012. "A monotonicity property for random walk in a partially random environment," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1369-1396.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1369-1396
    DOI: 10.1016/j.spa.2012.01.006
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    Cited by:

    1. Pham, Cong-Dan, 2019. "Some results on regularity and monotonicity of the speed for excited random walks in low dimensions," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2286-2319.

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