Markov Chains on Graphs and Brownian Motion

Nathanaël Enriquez; Yuri Kifer

doi:10.1023/A:1011119932045

Markov Chains on Graphs and Brownian Motion

Nathanaël Enriquez^*
, Yuri Kifer

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We consider random walks with small fixed steps inside of edges of a graph script G sign, 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 script G sign constructed in Ref. 1.

Original language	English
Pages (from-to)	495-510
Number of pages	16
Journal	Journal of Theoretical Probability
Volume	14
Issue number	2
DOIs	https://doi.org/10.1023/A:1011119932045
State	Published - 2001

Keywords

Brownian motion on graphs
Invariance principle
Random walks

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KW - Invariance principle

KW - Random walks

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Markov Chains on Graphs and Brownian Motion

Abstract

Keywords

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