Joel Zinn
(Photo courtesy of Texas A&M University)

We mark the passing of Dr. Joel Zinn, Professor Emeritus of Mathematics, Texas A&M University, on December 5, 2018, at his home in Westlake Village, California. He was 72 years old.

Joel was born on March 16, 1946, in Brooklyn, New York. His family said, about Joel’s early attraction to the subject, “He fell in love with mathematics at an early age, determining in the sixth grade that it would become his life’s work.” Having graduated from high school at 16, Joel earned his bachelor’s degree in mathematics from Queens College. While there, he met Michele; they married in 1968 and moved to Madison, Wisconsin, for Joel to pursue his PhD in Mathematics under Jim Kuelbs. Joel’s early career took him to the University of Minnesota, University of Massachusetts and Michigan State; in 1981, he became Associate Professor at Texas A&M, where he would remain for 36 years, becoming Professor Emeritus in 2007.

By 1978, Joel had published five papers, three as sole author. Topics included 0–1 laws, stable measures, translation of measures on vector spaces, recurrence in stationary sequences. During ’78–’81, he published 13 more papers on topics including: probability on Lp spaces, stable laws, iterated logarithm laws on Banach spaces, weighted empirical logarithm, limit theorems in Banach spaces, and random sets.

Many mathematicians will have shared the experience of having been caught up in a mathematical question, thrilled to the point where they lost track. Joel spent a lot of time in such a world, making his choices, innovating mathematical results. Excellence is about getting particular things done and bearing up when something doesn’t work. Working with others is in many cases essential if progress is to be made. It can be a highly efficient and supportive culture.

Joel was earning a reputation for steady production of fundamental research published in top journals, working and communicating with an impressive list of strong researchers. Joel co-authored 22 publications with Evarist Giné (who passed away in 2015).

As of today, Joel’s most highly cited publication is the 61-page 1984 Annals of Probability Special Invited Paper, co-authored with Giné: “Some limit theorems for empirical processes.” In some important parts, it was their improvement of basic results underpinning existing proofs that made the difference. When structuring the paper, they adopted spare, non-ambiguous notation and a narrative of examining years of advances on this topic by luminaries in probability theory, some of it unpublished work by Le Cam. Their treatment of details, old and new, is refreshing, accurate, author credited, and powerful. They had discovered ways to get a handle on the performance of empirical probabilities of events used as estimates of their actual probabilities, for all events in unusually large classes of events. Such results were particularly needed to support the role of Bootstrap in complex problems. Not to be overlooked are passages that give one the feel of being in the same room with lots of people you admire.

As the list of Joel Zinn’s different co-authors expanded, so too did the scope of his research topics. Most remained in the category of basic research, partly because fundamentals he continually worked were designed to punch through roadblocks standing in the way of developing broadly applicable mathematical formulas. His later topics included: uniform convergence of weighted kernel density estimators, various laws of iterated logarithm, a central limit theorem for empirical processes involving time dependent data, and when is the Student t-statistic asymptotically standard normal?

Another highly cited publication is Joel’s 1990 paper, again co-authored with Evarist Giné: “Bootstrapping general empirical measures.” Building on the ’84 paper, it was timely, represented an important commitment of probability talent, and genuinely extended the role of Bootstrap to complex probability models of current interest today. These results, not so many years after Bootstrap burst forth, elevated yet another part of probability to a higher level of mathematical maturity, clarity, generality, and leadership.

Joel’s many substantive publications, including his co-authorship (with V. Koltchinskii, R. Nickl, S. van de Geer and J. Wellner) of an obituary for Evarist Giné, often share elements of acute clarity, precise notation, wonderful narratives, and complete airing of important strengths and weaknesses of component parts.

Considering the pace of development, it seems that much of our precious Probability is carried around in the heads of those in the network of knowledgeable persons working that ground, many of whom are close at hand from shared academic ancestry. Like art and music, our subject will change over time. What is timeless is the value of colleagues like Joel Zinn who leave things in proper order for those who follow.

We close with a Toast: To Probabilists, Joel Zinn, et al.”

Written by Raoul LePage, Michigan State University