Boris Pittel

On spreading a rumor

Suppose that one of n people knows a rumor. At the first stage, he passes the rumor to someone chosen at random; at each stage, each person already informed (“knower”) communicates the rumor to a person chosen at random and independently of all other past and present choices. Denote by

Sudden Emergence of a Giantk-Core in a Random Graph

S_n

Note on the heights of random recursive trees and random m ‐ary search trees

the random number of stages before everybody is informed. How large is

Closed Exponential Networks of Queues with Saturation: The Jackson-Type Stationary Distribution and Its Asymptotic Analysis

S_n

Bootstrap percolation on the random regular graph

typically? Frieze and Grimmet, who introduced this problem, proved that, in probability,

On tree census and the giant component in sparse random graphs

S_n /( \log _2 n + \log n ) \to 1

On growing random binary trees

. In this paper we show that, in fact,

The first cycles in an evolving graph

S_n = \log _2 n + \log n + O( 1 )

Analysis of the space of search trees under the random insertion algorithm

in probability. Our proof demonstrates that the number

Asymptotic enumeration of sparse graphs with a minimum degree constraint

I( t )