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Critical random graphs: Diameter and mixing time. (English) Zbl 1160.05053
The mixing time of a random walk on a graph is defined as the waiting time $$t$$ for closeness between the t-step transition probabilities and the stationary probabilities. For a random graph $$G(n,p)$$, its largest connected component $$C$$ and the mixing time of a random walk on $$C$$ are investigated. The diameter of $$C$$ and the mixing time are specified for $$p$$ in the vicinity of $$1/n$$. Generalizations to graphs with bounded degrees are also considered.

##### MSC:
 05C80 Random graphs (graph-theoretic aspects) 82B43 Percolation 60C05 Combinatorial probability
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