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# Richard Dudley, professor emeritus of mathematics, dies at 81

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 (32at 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 theAdvancement 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 Berkley 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.