Celebratio Mathematica

Thomas Milton Liggett

Tom Liggett, some brief reflections

by Geoffrey R. Grimmett

Tom and Chris Liggett in Beijing, 2009.

The 1970s and 1980s were ex­cit­ing years for spa­tial prob­ab­il­ity mod­els. Few people were as in­volved in all that as was Tom, and his name will al­ways be as­so­ci­ated with in­ter­act­ing particle sys­tems. His 1985 mono­graph1 was a mile­stone — a sys­tem­at­ic ac­count of a the­ory, ini­ti­ated in the US by Frank Spitzer and de­veloped by Tom and oth­ers, that spanned cer­tain prob­ab­il­ist­ic mod­els arising in phys­ics, in fact around five such mod­els. It had an in­vig­or­at­ing ef­fect on prob­ab­il­ity world­wide, and it re­mains one of my bibles. I claim to have been the first pay­ing cus­tom­er for Tom’s volume, in a private view­ing ar­ranged by Spring­er New York.

Tom and I came to know one an­oth­er much bet­ter in later years. Our friend­ship began in the lec­ture room, where else? Each sat through a num­ber of lec­tures by the oth­er, and this led to ex­changes of views, and ul­ti­mately a warm and (for me) a greatly val­ued friend­ship. Tom was a mas­ter­ful lec­turer in the chalk­board tra­di­tion. Of a lec­ture of his that I at­ten­ded at Cor­nell in the early 1990s, I re­call ab­so­lutely noth­ing bey­ond the com­pel­ling sense of theatre as the math­em­at­ics un­fol­ded. The board was the stage, the math­em­at­ic­al ob­jects the play­ers, and the in­tel­lec­tu­al strands provided the plot — this was such skill with a stick of chalk.

Tom vis­ited Cam­bridge in 1993 for a pro­gram at the then re­cently es­tab­lished New­ton In­sti­tute. A num­ber of as­pects of life in Cam­bridge (in­clud­ing the bathing ar­range­ments) caused some be­muse­ment to vis­it­ors from the New World, as we pondered hard on the math­em­at­ics of in­ter­act­ing particle pro­cesses and ran­dom me­dia.

To mark Tom’s 65th birth­day in 2009, Day­ue Chen in­vited a num­ber of stu­dents, friends, and col­leagues to a very en­joy­able meet­ing in Beijing. The tim­ing was slightly un­for­tu­nate ow­ing to the H1N1 in­flu­enza epi­dem­ic then af­flict­ing China. There were a small num­ber of mys­ter­i­ous in­com­mu­nic­ado ab­sences, at­trib­uted to com­puls­ory quar­ant­ine on ar­rival in China, but Tom and Chris made it. It was an ex­cit­ing week, es­pe­cially for din­ners. Tom’s legs sur­vived the Great Wall hike at Jin­shan­ling by cour­tesy of the zip­line des­cent at Simatai. Vla­das Sidoravi­cius flew in just for the group photo.

In more re­cent years, Rosine and I were very happy to vis­it Tom and Chris (on one oc­ca­sion with Amy) at their house in Santa Mon­ica. Their do­mest­ic life was warm and lov­ing, and their garden gave them spe­cial pleas­ure (and gave us black-eyed susans).

Tom was a so­ci­able, frank, and mod­est per­son with strong ex­pect­a­tions of him­self and oth­ers. He had the highest of math­em­at­ic­al stand­ards, sup­por­ted by a nat­ur­al abil­ity that ex­ten­ded over both gen­er­al the­ory and com­plex cal­cu­la­tion. He was gen­er­ous with his time and re­spec­ted by all, and much loved by those close to him.

Of his many works bey­ond in­ter­act­ing particle sys­tems, I want to men­tion two that I es­pe­cially like. The first is his beau­ti­ful pa­per of 2009 with Ju­li­us Bor­cea and Pet­ter Brändén on the elu­sive and fas­cin­at­ing top­ic of neg­at­ive de­pend­ence, in which they in­tro­duce the concept of a strongly Rayleigh meas­ure.2 The second is his sur­pris­ing art­icle of 2016 with Al­ex­an­der Hol­royd cla­ri­fy­ing the re­la­tion­ship between sta­tion­ary se­quences that are fi­nitely de­pend­ent and those that are block factors.3 Each is re­fined and deeply clev­er.

Geof­frey Grim­mett is pro­fess­or emer­it­us of math­em­at­ic­al stat­ist­ics at the Stat­ist­ic­al Labor­at­ory, Centre for Math­em­at­ic­al Sci­ences, Cam­bridge Uni­versity.