On Random Walks in Random Environment on Trees and Their Relationship with Multiplicative Chaos

  • Mikhail Menshikov
  • Dimitri Petritis
Conference paper
Part of the Trends in Mathematics book series (TM)


The purpose of this paper is to report on recent results concerning random walks in a random environment on monochromatic and coloured trees and their relationship with multiplicative chaos. The proofs are omitted since they are extensively given elsewhere [12]. It is worth noticing that for the random walk on monochromatic tree the results we give were previously known [11]; we provide however a totally new proof, based solely on multiplicative chaos results, that allows to relax some stringent conditions on independence properties of the random transition probabilities. For the random walk on a coloured tree the results are new; the classification of the asymptotic behaviour of the random walk allows to obtain some hints for the classification of the yet unsolved corresponding multiplicative chaos problem.


Random Walk Random Environment Random String Coloured Tree Reversible Markov Chain 
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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Mikhail Menshikov
    • 1
  • Dimitri Petritis
    • 2
  1. 1.Department of Mathematical SciencesUniversity of DurhamUK
  2. 2.IRMARUniversitéde Rennes IRennes CedexFrance

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