Seminars & Colloquia Calendar
Linear cover time is exponentially unlikely
: Quentin Dubroff (Rutgers University)
Location: Hill Center Room 705
Date & time: Monday, 08 November 2021 at 2:00PM - 3:00PM
Abstract: 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 n-vertex 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.