A random walk on the Rado graph
Abstract
The Rado graph, also known as the random graph G(∞, 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 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.
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