Journal of Theoretical Probability

, Volume 14, Issue 2, pp 495–510 | Cite as

Markov Chains on Graphs and Brownian Motion

  • Nathanaël Enriquez
  • Yuri Kifer
Article

Abstract

We consider random walks with small fixed steps inside of edges of a graph \({\mathcal{G}}\), prescribing a natural rule of probabilities of jumps over a vertex. We show that after an appropriate rescaling such random walks weakly converge to the natural Brownian motion on \({\mathcal{G}}\) constructed in Ref. 1.

random walks invariance principle Brownian motion on graphs 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Nathanaël Enriquez
    • 1
  • Yuri Kifer
    • 2
  1. 1.Laboratoire de ProbabilitésUniversité de Paris 6ParisFrance
  2. 2.Institute of MathematicsHebrew UniversityJerusalemIsrael

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