Recurrent Random Walk and Logarithmic Potential

  • Frank Spitzer
Part of the Progress in Probability book series (PRPR, volume 28)


This is an attempt to show that a potential theory is associated with certain recurrent Markov processes in a natural way. For transient Markov processes this fact has been studied intensely. Thus Hunt [9] bases a general potential theory on transient continuous parameter processes, Doob [7] and Hunt [10] use the theory to construct boundaries for discrete parameter processes, Itô and McKean [11] solve the problem of characterizing the recurrent sets for simple random walk in three and higher dimension within the framework of the associated potential theory.


Random Walk Green Function Potential Theory Harmonic Measure Probability Interpretation 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Frank Spitzer
    • 1
  1. 1.University of MinnesotaUSA

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