Linear cover time is exponentially unlikely
Linear cover time is exponentially unlikely

Quentin Dubroff, Rutgers University
Fine Hall 224
InPerson Talk
Proving a 2009 conjecture of Itai Benjamini, we show: For any C, there is a > 0 such that for any simple random walk on an nvertex graph G, the probability that the first Cn steps of the walk hit every vertex of G is at most exp[an]. A first ingredient of the proof is a similar statement for Markov chains in which all transition probabilities are less than a suitable function of C. Joint with Jeff Kahn.