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Vertex-reinforced jump processes on trees and finite graphs
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  • Published: 12 November 2003

Vertex-reinforced jump processes on trees and finite graphs

  • Burgess Davis1 &
  • Stanislav Volkov2 

Probability Theory and Related Fields volume 128, pages 42–62 (2004)Cite this article

  • 142 Accesses

  • 25 Citations

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Abstract

We study the continuous time process on the vertices of the b-ary tree which jumps to each nearest neighbor vertex at the rate of the time already spent at that vertex times δ, plus 1, where δ is a positive constant. We show that for fixed b>1, if δ is large enough the process is transient, and if δ is close enough to zero it is recurrent. Related results for some other graphs and trees are also proved.

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Authors and Affiliations

  1. Department of Statistics, Purdue University, West Lafayette, IN 47907, USA

    Burgess Davis

  2. Department of Mathematics, University of Bristol, Bristol, BS81TW, UK

    Stanislav Volkov

Authors
  1. Burgess Davis
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  2. Stanislav Volkov
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Corresponding author

Correspondence to Burgess Davis.

Additional information

The research is partly supported by The Nuffield Foundation.

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Cite this article

Davis, B., Volkov, S. Vertex-reinforced jump processes on trees and finite graphs. Probab. Theory Relat. Fields 128, 42–62 (2004). https://doi.org/10.1007/s00440-003-0286-y

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  • Received: 20 November 2002

  • Revised: 22 May 2003

  • Published: 12 November 2003

  • Issue Date: January 2004

  • DOI: https://doi.org/10.1007/s00440-003-0286-y

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Keywords

  • Time Process
  • Positive Constant
  • Continuous Time
  • Related Result
  • Jump Process
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