My first contact with Liggett’s ideas was in 1981, when his student “Coupling the simple exclusion process” (Ann. Probability 4:3 (1976), 339–356) and said: “You should read from here to here”, a couple of pages containing this paragraph:came to São Paulo, handed me a copy of the paper
Another important property of the coupled process can be seen most clearly by thinking of it as a process in which the particles which move on \( S \) are of four types: \( (0,0) \), \( (1,1) \), \( (0,1) \), \( (1,0) \). Then some of the transitions can be though of as resulting in the destruction of the particles of the last two types and their replacement by particles by the first two types. Therefore the “number” (which is usually infinite) of particles of the first two types can only increase.
This early contact with the basic coupling was incredibly influential for me. I used it in my doctoral thesis and then worked on the simple exclusion process for many, many years building on this beautiful coupling construction. The \( (1, 0) \) particles were later called second class particles and played a crucial role in the interplay between the simple exclusion process, the Burgers equation and the last passage percolation growth model, including the KPZ boom. Tom’s 1985 interacting particle systems book, called the yellow book by my young daughters, has been around me ever since.
I first met him personally at Dartmouth College in 1984, during a workshop organized by. I was a postdoc fellow at Rutgers and was looking at all those probability monsters with admiration. Tom approached and said with a perfect Argentinian accent “¿Hola, trabajas con Enrique en São Paulo?” He learned the language during his childhood in Buenos Aires while his father was a pastor of the Disciples of Christ church at Zapiola Street, a few blocks away from my current home. Tom came to the city again in the 90s and was very touched by a visit to one of his closest friends from that time.
I have two papers with Tom: one withabout the time needed by the symmetric simple exclusion process to empty a box, and the other with and with a correlation inequality for the contact process. Most of my coauthors sit with me in front of a blackboard for hours waiting for an idea to pop up. With Tom it was different. He would listen to your problem, say that he will think about it and a few days later reappear with a completely written solution. He liked solo thinking, but he was always curious and supportive of alternative approaches. We were at Les Houches in 1992, participating in a mathematical physics meeting where many talks were very far from probability; however Tom attended all the talks.
In 2000 Tom gave a talk at the annual probability school EBP (Escola Brasileira de Probabilidade) in Mambucaba (Angra dos Reis, Brasil), and at lunch time some participants were discussing online publications. A major catastrophe could turn off all computers, erasing electronic journals and books, but paper journals would always be accessible, argued Tom. Remembering his comment today while looking at the yellow book, I realize that he was writing his papers not only for our contemporary community, but with an eye to the mathematical readers of the future.
Pablo A. Ferrari is a Professor in the Department of Mathematics at the Universidad de Buenos Aires in Buenos Aires, Argentina.