My contribution to this celebration of Tom Liggett’s mathematical life is a personal one, reflecting the enormous debt I owe. With the rest of the community I mourn his recent passing.
Tom’s foundational work on particle systems culminated in his book Interacting Particle Systems.1 With and Brownian motion and continuous martingales2 it is the most important book in my life. The book begins with two chapters assembling an array of tools that is a helpful source for workers in other probabilistic fields. It then treats in turn the individual particle systems, mapping out the different techniques needed to analyse them. What was extremely useful to me and other young researchers was the end of chapter lists, with short discussions, of the systems’ open problems. Short analyses were given of where a direct application of the ideas introduced in the chapter ran into trouble. This communicates like a direct conversation the limits of the techniques and the boundaries of current knowledge. I am unaware of a book of comparable level that has this feature. There must be many people who never met Tom but benefited immeasurably from his book.
Though I only wrote two papers with Tom, his ideas and clear targeted advice contributed to many others. In one of our first mathematical conversations, on my thesis which was far from his work, it was obvious that his understanding was on a higher level. Somewhat humiliating but enriching. Tom’s matter of fact precision inevitably opened up doors. But Tom’s influence was global. The conference in Beijing celebrating his 65th birthday, hosted by, was a fitting appreciation from the many who had made careers in the field which he had helped to build.
A final memory is of Tom saying, while we were discussing some question, that “I think about probability in the same way as you”. I didn’t and don’t think this was true.
Thomas Mountford is Chair of Stochastic Processes at the École Polytechnique Fédérale de Lausanne in Lausanne, Switzerland.