John Gray Aldous

John Gray M'Kendrick, physiologist (1841-1926).

IN 1859 The British Association met in Aberdeen. A letter' circulated in February of that year, asked for contributions to the Natural History exhibition suggesting that '. . . iftolerably complete (as a little exertion may easilymake it) will prove very interesting and instructive.' M'Kendrick was then an indentured clerk in a lawyers' office, and had assembled a marine aquarium in his lodging...

The vision of Aldous Huxley

Asymptotic Behavior of Aldous’ Gossip Process

Aldous (2007) defined a gossip process in which space is a discrete N ×N torus, and the state of the process at time t is the set of individuals who know the information. Information spreads from a site to its nearest neighbors at rate 1/4 each and at rate N−α to a site chosen at random from the torus. We will be interested in the case in which α < 3, where the long range transmission significa...

Proof of Aldous’ Spectral Gap Conjecture

Aldous’ spectral gap conjecture asserts that on any graph the random walk process and the random transposition (or interchange) process have the same spectral gap. We prove the conjecture using a recursive strategy. The approach is a natural extension of the method already used to prove the validity of the conjecture on trees. The novelty is an idea based on electric network reduction, which re...

The Aldous-Shields model revisited (with application to cellular ageing)

In Aldous and Shields (1988), a model for a rooted, growing random binary tree was presented. For some c > 0, an external vertex splits at rate c−i (and becomes internal) if its distance from the root (depth) is i. For c > 1, we reanalyse the tree profile, i.e. the numbers of external vertices in depth i = 1, 2, .... Our main result are concrete formulas for the expectation and covariance-struc...