2022/05/13 by Chatterjee, Sourav, Diaconis, Persi, Miclo, Laurent
#Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO) #Probability (math.PR)
paper · doi:10.48550/arxiv.2205.06894
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 log2^*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.