A random walk on the Rado graph

Sourav Chatterjee; Persi Diaconis; Laurent Miclo

A random walk on the Rado graph

Probability 2022-05-17 v1 Combinatorics Logic

Authors: Sourav Chatterjee , Persi Diaconis , Laurent Miclo

Abstract

The Rado graph, also known as the random graph $G(\infty, p)$ , is a classical limit object for finite graphs. We study natural ball walks as a way of understanding the geometry of this graph. For the walk started at $i$ , we show that order $\log_2^*i$ steps are sufficient, and for infinitely many $i$ , necessary for convergence to stationarity. The proof involves an application of Hardy's inequality for trees.

Keywords

random walk on graphs random walk in random environment random walks

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@article{arxiv.2205.06894,
  title  = {A random walk on the Rado graph},
  author = {Sourav Chatterjee and Persi Diaconis and Laurent Miclo},
  journal= {arXiv preprint arXiv:2205.06894},
  year   = {2022}
}

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43 pages

A random walk on the Rado graph

Abstract

Keywords

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