Continuous-time random walks on networks have large-deviation properties for the number of distinct visited nodes that are governed solely by waiting-time statistics at small times, independent of topology.
The range of stable random walks.The Annals of Probability, 19(2):650–705, 1991
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Network exploration by random walks: A large deviation perspective
Continuous-time random walks on networks have large-deviation properties for the number of distinct visited nodes that are governed solely by waiting-time statistics at small times, independent of topology.