Celebratio Mathematica

Thomas Milton Liggett

Tribute to Thomas Liggett

by Maria Eulália Vares

It was in 1981, dur­ing a short vis­it from En­rique D. An­djel to the In­sti­tuto de Matemática Pura e Ap­licada (IMPA) in Rio de Janeiro that I was first ex­posed to Tom Lig­gett’s work. En­rique and I had both fin­ished the Ph.D. more or less at the same time, he with Tom at UCLA and I at Berke­ley, with Warry Mil­lar, and we had just star­ted work­ing in Brazil. The sub­ject of Tom’s re­search was totally new and very ex­cit­ing to me. It be­came clear that I should learn more, and try to work more closely with the loc­al team in in­ter­act­ing particle sys­tems (con­cen­trated in São Paulo at that time). I could not travel much dur­ing that peri­od, and so was un­able to at­tend sev­er­al con­fer­ences. Tom’s pa­pers and the mas­ter­piece In­ter­act­ing Particle Sys­tems1 were truly fun­da­ment­al for my un­der­stand­ing of the the­ory, for help­ing me to learn about the main prob­lems, and es­pe­cially for most of the ex­amples that mo­tiv­ated our re­search group, in­clud­ing the de­vel­op­ment of ideas in meta­sta­bil­ity, for which we used the con­tact pro­cess as a ba­sic ex­ample. I well re­mem­ber writ­ing to Tom about one or an­oth­er point in the book (also in the second volume) which did not seem so clear to me, and re­ceiv­ing his kind an­swer by email.

In 1997, Tom vis­ited Rio de Janeiro, as plen­ary speak­er of the Brazili­an Col­loqui­um in Math­em­at­ics held at IMPA. I think he liked it, as three years later he re­turned for the fourth edi­tion of the Brazili­an School of Prob­ab­il­ity, which took place in a re­laxed am­bi­ence, next to the beach in Mam­bu­caba. That school was truly fant­ast­ic; I still re­mem­ber Tom’s lec­ture on the role of con­di­tion­ing and coup­ling in in­ter­act­ing particle sys­tems.

I was giv­en the mar­velous op­por­tun­ity in 2009 to par­ti­cip­ate in the cel­eb­ra­tion of Tom’s 65th birth­day in Beijing. It was an ex­tremely happy oc­ca­sion; we all cel­eb­rated that birth­day with Tom and Chris in a won­der­ful at­mo­sphere, with de­li­cious food, the ad­ven­ture of a walk on the Great Wall for all the brave par­ti­cipants (Tom in­cluded), all this merged with days of in­tense and ex­cit­ing talks. It is an event that oc­cu­pies a great place in my memory.

The next oc­ca­sion for me to meet Tom was the cel­eb­ra­tion of his 75th birth­day in a very beau­ti­ful and warm event at UCLA, in March 2009. His health did not al­low him to ac­tu­ally come to the meet­ing, but we could cel­eb­rate his achieve­ments.

Bey­ond his re­mark­able work in prob­ab­il­ity, Tom was a great ment­or for many prob­ab­il­ists of at least two or three gen­er­a­tions. I was ex­tremely lucky to have met him.

Maria Eu­lalia Vares is a pro­fess­or at the In­sti­tuto de Matemática, Uni­ver­sid­ade Fed­er­al do Rio de Janeiro.