In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributionalâ€¦ (More)

In 1924 Yule observed that distributions of number of species per genus were typically long-tailed, and proposed a stochastic model to fit these data. Modern taxonomists often prefer to representâ€¦ (More)

Abstracr-When several users simultaneously transmit over a shared communication channel, the messages are lost and must be retransmitted later. Various protocols specifying when to retransmit haveâ€¦ (More)

We study the following model for a phylogenetic tree on n extant species: the origin of the clade is a random time in the past whose (improper) distribution is uniform on (0, âˆž); thereafter, theâ€¦ (More)

Start two independent copies of a reversible Markov chain from arbitrary initial states. Then the expected time until they meet is bounded by a constant times the maximum first hitting time for theâ€¦ (More)

We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists andâ€¦ (More)

For simple random walk on a finite tree, the cover time is the time taken to visit every vertex. For the balanced b-ary tree of height m, the cover time is shown to be asymptotic to 2mb(log b)/(bâˆ’ 1)â€¦ (More)

Chatterji [2] has formulated the following heuristic principle: given any limit property for independent identically distributed random variables (i.i.d.r.v.'s), there exists an analogous propertyâ€¦ (More)