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math.PR2010
Linear Cover Time is Exponentially Unlikely
Itai Benjamini, Ori Gurel-Gurevich, Ben Morris
We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small. More precisely, for every D and C, there exists…
math.PR2010
Tightness of Fluctuations of First Passage Percolation on Some Large Graphs
Itai Benjamini, Ofer Zeitouni
The theorem of Dekking and Host regarding tightness around the mean of first passage percolation on the binary tree, from the root to a boundary of a ball, is generalized to a clas…