# Richard M. Dudley 1938-2020

Professor Emeritus of Mathematics

Published: January 31, 2020; Updated: February 14, 2020

Richard Mansfield Dudley, MIT professor emeritus of mathematics, died on Jan. 19 following a long illness. He was 81. Dudley served on the MIT mathematics faculty from 1967 until 2015, when he officially retired. Over the course of those 48 years, during which he published over 100 articles as well as numerous books and monographs, he made fundamental breakthroughs in the theory of stochastic process and the general theory of weak convergence.

Dudley’s work, starting in the 1960s, shaped the fields of probability,
mathematical statistics, and machine learning, with highly influential
contributions to the theory of Gaussian processes and empirical processes.
What is now widely known as “Dudley’s entropy bound” has become a standard
tool of modern research in probability, statistics, and machine learning.
Dudley’s work also had a transformative impact on the theory of empirical
processes initiated by Vladimir Vapnik and Alexey Chervonenkis in the
context of machine learning. Over a series of papers, starting with his
landmark paper “Central limit theorems for empirical processes”
(*Annals of Probability*, 1978) and culminating with his influential
Saint-Flour lecture notes (1984) and later, his book “Uniform Central Limit
Theorems” (Cambridge University Press, 1999), Dudley distilled and developed
these ideas into an actionable theory that still today is the reference
framework in mathematical statistics and statistical learning theory. The
larger communities of probability and statistics remember his excellent
taste for mathematically rich and impactful subjects, as well as his highest
standard of rigor.

Dudley gave a number of distinguished research talks. He was an invited speaker at the 1974 International Congress of Mathematicians as well as at meetings of the American Mathematical Society, the Institute of Mathematical Statistics, and the Bernoulli society. He was also an invited lecturer at Saint-Flour probability summer school in probability in 1982 and several of the Vilnius Conferences on Probability Theory and Mathematical Statistics. He was a regular participant and organizer of several conferences and meetings, including Probability in Banach Spaces.

In 1976, Dudley visited the University of Aarhus, and there produced a set
of graduate lecture notes, “Probabilities and Metrics.” These were to become
a part of his graduate text, “Real Analysis and Probability,” published by
Wadsworth, Inc. in 1989. An early review of this work in the
*London Mathematical Society Bulletin* (July 1990) found that it
“could be compared to the appearance of Breiman or Loève's classic
probability texts.” The text has since become a standard, and in 2002 was
reissued by Cambridge University Press and continues to be in print.

Dudley was always highly regarded as a graduate mentor throughout his career. He advised 33 PhD candidates (32 at MIT), yielding some 105 academic “descendants.”

Dudley served the scholarly community as associate editor (1972-78) and then
chief editor (1979-81) of *Annals of Probability*. He was a member of
the editorial board of the
*Wadsworth/Brooks/Cole Advanced Series in Statistics/Probability*from
1982 to 1992. For many years while on the MIT faculty, Dudley worked with
the MIT Science Library in overseeing their collection of mathematical
journals. He sought to explain to the faculty how the library's budget
decisions were reached, to help them effectively express their research
needs.

Among his honors, Dudley was an Alfred P. Sloan Research fellow from 1966-68 and Guggenheim Foundation Fellow in 1991. He was selected to serve on the honorary Advisory Board of Stochastic Processes and their Applications from 1987-2001. In 1993, Dudley was elected a fellow of the American Statistical Association, “for world-recognized contributions to probability theory with far-reaching consequences for statistics, for founding the modern theory of empirical processes, and for dedication to many successful PhD students.” He was also elected fellow of the Institute of Mathematical Statistics, the American Association for the Advancement of Science, and the American Mathematical Society and was selected to be a member of the International Statistical Institute.

Born on July 28, 1938, in Cleveland, Ohio, Dudley completed a BA from Harvard University, summa cum laude, in 1959. He wrote a doctoral dissertation under two advisors at Princeton University, Gilbert A. Hunt and Edward Nelson, completing his PhD in mathematics in 1962. He was an instructor at the University of California at Berkeley in 1962-63, and an assistant professor from 1963 to 1967, before moving to MIT.

Dudley is survived by his wife, Elizabeth (Liza) Martin; his sisters, Edith D. Sylla and Alice D. Carmel; brother-in-law Richard E. Sylla; and nieces Anne Sylla, Margaret S. Padua, and Genevieve Carmel.

Memorial contributions may be made in Dudley's name to the Environmental Defense Fund or to Partners in Health.