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Positive Harmonic Functions of Transformed Random Walks

  • Behrang Forghani
  • Keivan Mallahi-Karai
Article
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Abstract

In this paper, we will study the behavior of the space of positive harmonic functions associated with the random walk on a discrete group under the change of probability measure by a randomized stopping time. We show that this space remains unchanged after applying a bounded randomized stopping time.

Keywords

Random walk Harmonic functions Martin boundary 

Mathematics Subject Classification (2010)

60J50 60B15 31C05 

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Notes

Acknowledgments

The authors wish to use the opportunity to thank Vadim Kaimanovich and Wolfgang Woess for numerous valuable suggestions on an earlier version of this paper. We also thank Sébastian Gouzël and Iddo Ben-Ari for fruitful discussions. During the completion of this project, the second author was partially supported by the DFG grant DI506/14-1.

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentBowdoin CollegeBrunswickUSA
  2. 2.Department of Mathematics and LogisticJacobs University of BremenBremenGermany

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