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Conditioned Two-Dimensional Simple Random Walk: Green’s Function and Harmonic Measure

Author

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  • Serguei Popov

    (University of Campinas – UNICAMP)

Abstract

We study the Doob’s h-transform of the two-dimensional simple random walk with respect to its potential kernel, which can be thought of as the two-dimensional simple random walk conditioned on never hitting the origin. We derive an explicit formula for the Green’s function of this random walk and also prove a quantitative result on the speed of convergence of the (conditional) entrance measure to the harmonic measure (for the conditioned walk) on a finite set.

Suggested Citation

  • Serguei Popov, 2021. "Conditioned Two-Dimensional Simple Random Walk: Green’s Function and Harmonic Measure," Journal of Theoretical Probability, Springer, vol. 34(1), pages 418-437, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00963-4
    DOI: 10.1007/s10959-019-00963-4
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