Attracting edge property for a class of reinforced random walks

Vlada Limic ^[1]
1. [1] University of British Columbia
  
  University of British Columbia
  
  Canadá
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 3, 2003, págs. 1615-1654
Idioma: inglés
DOI: 10.1214/aop/1055425792
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Resumen
- Using martingale techniques and comparison with the generalized Urn scheme, it is shown that the edge reinforced random walk on a graph of bounded degree, with the weight function W(k)=kρ,ρ>1, traverses (crosses) a random attracting edge at all large times. If the graph is a triangle, the above result is in agreement with a conjecture of Sellke.