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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The research is partly supported by The Nuffield Foundation.
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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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DOI: https://doi.org/10.1007/s00440-003-0286-y