Celebratio Mathematica

Thomas Milton Liggett

In memory of Thomas Liggett

by Thomas Mountford

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 Re­vuz and Yor’s 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 Day­ue Chen, 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.