A random walk on the Rado graph

Sourav Chatterjee (1) , Persi Diaconis (1) , Laurent Miclo

1 Stanford University

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.

Domaines: Probabilités [math.PR]

Sourav Chatterjee, Persi Diaconis, Laurent Miclo. A random walk on the Rado graph. Harold Widom Memorial Volume, Birkhäuser/Springer Nature, In press. ⟨hal-03777224⟩