One frog is awake at the root of a d-ary tree of height n, and Poi(m) frogs are asleep at every other vertex. Awakened frogs move as simple random walks, waking any sleeping frogs they encounter. I'll discuss two questions posed by Itai Benjamini: Is the cover time (the first time that all vertices have been visited) polynomial in n? And does the cover time undergo a phase transition in m? We partially answer the first question by showing that the cover time is n log n when m is large. We show that the answer to the second question is yes, as the cover time is at least n^2 when m is small. Joint work with Christopher Hoffman and Matthew Junge.
Biography
Tobias Johnson got his Ph.D. from the University of Washington in 2014, advised by Ioana Dumitriu and Soumik Pal. He was a postdoc for a year and a half at the University of Southern California working with Larry Goldstein, is currently a postdoc at NYU working primarily with Joel Spencer, and starts a permanent job in September at the College of Staten Island (CUNY).