by Jim Pitman
Professor and
John Rice
Department Chair

On the heels of being awarded the Chair of the Class of 1940 here at Berkeley, David Aldous has been awarded an honorary degree of Doctor of Science by the Board of Trustees of the University of Chicago! They cite his "contributions of great importance to the fields of mathematical probability, applied probability, and to the theory of computing."

David Aldous has been a faculty member at Berkeley since 1979. During this time he has gained a reputation as one of the world's leading probabilists. In the international community of research workers in probability theory and stochastic processes, Aldous's work is regarded as deep, innovative and influential. His early work on exchangability and the subsequence principle gained him immediate recognition in the late 70's which led to his original appointment at Berkeley. Since then he has made a deep impression in several other areas of probability theory: rates of convergence to equilibrium in finite-state Markov chains, Poisson approximations in diverse contexts, probabilistic analysis of algorithms, the study of random trees and graphs, and the analysis of coalescent processes. His worked is marked by great conceptual insight, originality of appproach, and technical skill. His bibliography contains 88 research papers, a research monograph Probability Approximations via the Poisson Clumping Heuristic, and he is currently working on a graduate level textbook about Markov chains and random walks on graphs.

In the field of Markov chains, Aldous showed that the time-reversible property shared by a great many chains of practical interest, such as random walks on graphs, implies that the ratios between various measures of the rate of convergence to equilibrium of such chains are bounded by universal constants. This striking and unexpected result, and the circle of ideas used to obtain it, has provided tools for analysis of a number of algorithms related to sampling and simulation of complex combinatorial objects of interest to computer scientists. Work of Aldous and his collaborators has led to a rebirth of interest in the whole subject of finite state Markov chains. His ideas have been adapted and applied by both statisticians and computer scientists through Monte Carlo Markov chain techniques.

A central theme of Aldous's research in the early 90's was random trees. The important role of tree structures in computer science has led to a great deal of interest in various kinds of random trees, at the interface of probability theory with analysis of algorithms. Aldous has been a conceptual pathbreaker in this field, with his talent for providing a deep conceptual understanding for the often delicate asymptotics involved in analyzing random trees with n verticesfor large n. His tour de force in this area is his series of three very substantial papers The continuum random tree I, II and III. To oversimplify with a single sentence, Aldous's continuum random tree (CRT) is a limiting object derived from random trees with n vertices just as Brownian motion is a limiting object derived from random walks with n steps. Both technically and conceptually there is much more to be said, which Aldous does in this brilliant series of papers. Because excursions of a random walk can be coded as trees, there are profound connections between the CRT and the theory of Brownian excursions, which Aldous has developed and applied to obtain remarkable results.

More recently, Aldous has worked on random graphs and coalescent processes. He has established deep connections between the phase transition known as "the birth of the giant component" in random graphs, and the theory of Brownian excursions. The basic link is provided by his own theory of random trees applied to the large trees which appear during the birth to the giant component. This deep work is typical of Aldous's greatest achievements: he has taken a difficult problem, of interest to a great many researchers, and built a conceptual framework in which to solve the problem. The solution has brought the whole subject to a new level of exploring the implications of his ideas.

While creating this remarkable body of research, Aldous has remained devoted to his teaching duties and departmental responsiblities. He has been an effective and inspiring teacher at all levels from the lower division to graduate courses. He has been the mentor of numerous graduate students. He has served the department in important committee positions: personnel, head graduate adviser, and admissions. Recently, he served as chair of the department for two years.

Outside the university, he has served the scientific community as an associate editor of various research journals, and as an adviser to the NSF, and as the organizer of numerous meetings and workshops. He has maintained a high profile through his frequent contributions at scientific meetings, and his regular acceptence of invitations to speak at other universities.

His achievements have been recognized in an array of the highest honors. In 1980 he was awarded the Rollo Davidson prize. In 1993 he was awarded the first Line and Michel Loève International Prize in Probability. The elaborate procedure used to award this prize ensures that its recipient is internationally acknowledged as the world's leading probabilist under 45 years of age. In 1993, Aldous was honored by the Institute of Mathematical Statistics as the Wald Lecturer at the I.M.S. annual meeting in San Francisco, where he gave a brilliant series of lectures on his work on random trees. In 1994 he was made a Fellow of the Royal Society, the most prestigious scientific institution of in the United Kingdom, and in 1998 he was an invited speaker at the International Congress of Mathematicians.

We are delighted by these recognitions of his remarkable achievements. Congratulations, David!

David Aldous

The Department celebrates with David Aldous.