# Obituary: Johannes Kemperman, 1924–2011

Johannes H.B. Kemperman’s research and teaching career of 50 years included ten years at Purdue, 25 years at the University of Rochester, and ten years at Rutgers. During this time he produced three major books, over 100 publications, and 23 PhD students. He was a Fellow of IMS and of the American Association for the Advancement of Sciences, and a Correspondent of the Royal Dutch Academy of Sciences. He served in editorial posts at the *Annals of Mathematical Statistics, Annals of Probability, Annals of Statistics, Stochastic Processes and their Applications*, and *Aequationes Mathematicae*. His wide research interests led to outstanding work in number theory, group theory, analysis including asymptotic expansions, functional equations, mathematical biology, probability, and statistics.

Johannes, or less formally, Joop (pronounced “Johp” in Dutch) was born in Amsterdam in 1924, the eldest of five children in a middle-class family. His mathematical ability led to his getting scholarships at the University of Amsterdam, where he received his BS in 1945, and PhD in 1950 in Mathematics/Physics. During World War II, he strongly opposed the Nazis, who occupied the Netherlands. He spent much of the war hiding in haylofts, reading mathematics.

After passing the PhD-qualifying “Doctoraal Examen” in 1948, he worked for three years full-time as a research associate in the Department of Applied Mathematics at the prestigious Mathematische Centrum in Amsterdam. Occasionally the Department would receive requests for help on applied problems, and Joop solved several groundwater flow problems posed by the Dutch waterworks. Most of the time Joop was free to work on his own research interests in number theory, pure analysis, probability and statistics. Joop got his PhD in Amsterdam, The Netherlands, on December 20, 1950. This was the beginning of an outstanding research career.

In 1951 Joop went on a Fulbright grant to the Mathematics Department at Purdue University, where he was subsequently offered a tenure track Assistant Professorship and became a Full Professor in 1959. In June 1953 Joop married Wilna Ypma from The Netherlands, whom he had known for five years, and after a brief honeymoon they returned to Purdue. They later had five children together: Steve, Bruce, Hubert, Ingrid and Eric.

At Purdue, probability and statistics were taught by the Math Department faculty. This teaching sparked Joop’s interest to the extent that about half of his career publications were in probability and statistics. A notable example was Joop’s 1956 Annals of Mathematical Statistics paper on generalized tolerance limits, that was stimulated by teaching a course in nonparametric statistics. Joop also began work on his classical monograph The First Passage Problem for a Stationary Markov Chain which he completed in 1959. Joop also continued his research in number theory and analysis.

In 1961 Joop was recruited to the Mathematics Department at the University of Rochester, later named as Fayerwether Professor. At the time there was not a separate statistics department. In 1963, Allen Wallis, a strong promoter of statistics departments, became Chancellor of the University of Rochester. In 1968 Jack Hall was recruited as chair of a new statistics department, and attracted excellent people. The Department, with a total of about six full-time equivalent lines, used partial lines for joint appointments, including Joop whose tenure remained in mathematics.

At Rochester, Joop was active in stimulating research in theoretical biology, mathematical economics, mathematical physics and operations research, in addition to his active program of teaching and research in mathematics and statistics. He was an active participant in developing policy and leadership in both of these departments.

In 1985 Joop retired from Rochester and joined the Statistics Department at Rutgers, and was also a full voting member of the Mathematics Department. Joop found Rutgers an exciting mathematical environment with stimulating talks and speakers. He did joint work with Art Cohen and Harold Sackrowitz in addition to his wide-ranging research.

A Rutgers Statistics seminar in 1992 by Joel Cohen stimulated a collaboration that led to a joint book that deals with many different ways to compare information channels. The 1998 book Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics, and Population Sciences, jointly with Joel Cohen and Gheorghe Zbaganu, is breathtaking in its perspectives, and was awarded the Gheorghe Lazăr Prize of the Romanian Academy in 2000. Joel notes how “Joop contributed many innovative and unexpected ideas and techniques. Joop’s creativity, combined with his broad mathematical background, came to the fore in the startling proofs…”

Joop was known for his willingness to listen and contribute to a great variety of mathematical problems. This trait is illustrated by his large number of co-authors, and the large number of mathematicians who cite his results. Once he became interested in a subject he often would investigate it in great detail. This shows itself in the large number of quite long papers of Joop’s, often with results spread out over years; see, for instance, his papers on information theory, or on distribution mod 1, or on moment problems.

An important contribution to probability theory, motivated by questions in statistics, and in particular to sequential analysis, deals with the exit time and exit place of a random walk *S _{n}* from a strip parallel to the time-axis. More generally Joop allows

*S*to be a Markov chain. Only rarely are explicit calculations possible, but Joop derived interesting and powerful methods to attack such problems. In coding theory, Joop found simple proofs and generalized basic results.

_{n}Some of the papers Joop was most proud of were in number theory, related group theory, and functional equations. Examples are his 1957 paper in the* Transactions of the American Mathematical Society* on a generalized functional equation, and his 1960 *Acta Math* paper dealing with small sumsets in Abelian groups. Throughout his career Joop was interested in the use of probability theory in number theory. In particular one finds a number of papers which apply probability to ‘distribution mod 1’.

Joop passed away on June 13, 2011, surrounded by family. Joop’s beloved Wilna had passed away in 1995. Joop is survived by four of his children—Bruce, Hubert, Ingrid and Eric—and three daughters-in-law, one son-in-law and eight grandchildren.

Joop was an exceptionally nice person and a true gentleman. He was a wonderful colleague and friend. We are all grateful that we had him with us for many years. He leaves a beautiful personal and professional legacy that will be cherished by all who knew him.

Written by Jack Hall and Joe Naus

*Some of this material is summarized from: Naus, J.I., “A conversation with Johannes H.B. Kemperman” Statistical Science 15 (November 2000) 396–408.*

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