by Sunder Sethuraman
Although I was not a formal student of Professor Tom Liggett, through various points of my career Tom was an important mentor. Always free to share knowledge, Tom was one to take time to answer questions and give careful advice when asked. Many careers, including mine, derive in part from his foundational research in the field of interacting particle systems.
My first introduction to Tom was through his book Interacting Particle Systems (1985). I was asked to go through it in 1992 as a graduate student at NYU starting PhD thesis research on exclusion and zero-range processes with Raghu Varadhan. Tom’s book was a constant companion then, often turned to Chapter 8, “The Exclusion Process”.
My thesis problem was to understand for which functions \( f \) the limiting variance of the scaled additive functional, \( \smash{\frac{1}{\sqrt{t}}}\int_0^t f(\eta_s)\,ds \), with respect to these interacting particle systems was finite. Such a result relates to the scaling behavior of a tagged, or distinguished, particle in these models, a concern of interest to Tom as well, who wrote on aspects of tagged particles in Interacting Particle Systems and also in his book Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (1999). I first corresponded with Tom in 1994, in the last year of my PhD, asking if he would serve as the primary advisor for an NSF postdoc application. Tom was kind to agree, and a proposal was written, but at the end the position didn’t materialize. We kept in touch though and later, while at Iowa State University, it was an honor to invite Tom to speak at the “Ames Workshop on Particle Systems”, April 2001, organized together with Timo Seppäläinen.
Tom’s energy, drive, and optimism were an inspiration. He once encouraged me early on when I was stuck in a research problem to investigate whether a term or small example could be computed, pointing out that such an effort might lead to a better outlook.
In a more recent encounter, Tom was excited to discuss his work on negative association and the exclusion process and his 2009 papers “Distributional limits for the symmetric exclusion process” and “Negative dependence and the geometry of polynomials” with Borcea and Brändén. He felt there might be application in what I was doing at the time. Indeed, these interesting results helped with some estimation in my paper, “Large deviations for the current and tagged particle in 1D nearest-neighbor symmetric simple exclusion” with Varadhan.
Like many, I was excited to attend Tom’s 75th birthday conference two years ago at UCLA in 2018, and was looking forward to chatting more with him again. Although he couldn’t be there in person, the occasion was a celebration of his scientific and personal impact, with a range of participants, from students to senior professors. At the banquet, it was wonderful to talk with Chris Liggett and to meet Tim and Amy, those to whom Interacting Particle Systems was dedicated.
Sunder Sethuraman is a professor in the Department of Mathematics at the University of Arizona.
