Celebratio Mathematica

It was my great priv­ilege to claim Tom Lig­gett as my friend for the 55 years since we met in Kai Lai Chung’s real ana­lys­is class dur­ing Tom’s first year as a Ph.D. stu­dent at Stan­ford. And it was my good luck that Tom elec­ted to join the UCLA fac­ulty where the short dis­tance between his of­fice and mine made it easy to in­ter­act, chat, go to lunch, and get an­swers to my ques­tions. Without Tom, my pro­fes­sion­al life would have been so much more dif­fi­cult.

When asked a math ques­tion, Tom in­vari­ably not only sup­plied the an­swer but did so in an easy-to-fol­low man­ner. He was a won­der­fully ad­ept teach­er even be­fore his form­al teach­ing at UCLA com­menced. His teach­ing skills em­an­ated from his in­terest in math­em­at­ics, his de­sire and will­ing­ness to of­fer help, his clar­ity of thought, and his amaz­ing math­em­at­ic­al prowess. Al­most al­ways, he could an­swer my many ques­tions on the spot, ques­tions I had labored on for days or weeks. I nev­er had a ques­tion he could not an­swer.

In 1969, we pub­lished our first joint pa­per en­titled “Stochast­ic games with per­fect in­form­a­tion and time av­er­age pay­off” in SIAM Re­view.1 The pa­per con­cerned a Tauberi­an the­or­em re­lat­ing time av­er­age and dis­coun­ted pay­offs which had been in­cor­rectly ex­ten­ded in the pre­vi­ous lit­er­at­ure. Tom eas­ily came up with the needed counter­example. Forty years later, we pub­lished our second joint pa­per. “The asymp­tot­ic Shap­ley value for a simple mar­ket game” ap­peared in Eco­nom­ic The­ory in 2009.2 The first proof Tom came up with fol­lowed dir­ectly from his Ph.D. thes­is, but the journ­al ed­it­or in­sisted that the proof not be based upon such a dif­fi­cult-to-loc­ate res­ult on the Browni­an bridge. Tom eas­ily found a new proof that fol­lowed from well known prin­ciples.

In the many years that I knew Tom, he was in­vari­ably up­beat, cheer­ful, and happy to as­sist. Between the time he ar­rived as an as­sist­ant pro­fess­or at UCLA and the time he mar­ried Chris, he would join us for din­ner two or so times per month. He was al­ways good com­pany. After their mar­riage, we con­tin­ued to dine and in­ter­act with Tom and Chris so­cially. In ad­di­tion, Tom and I played hand­ball weekly for a dec­ade or more. Un­be­knownst to most, Tom was a pretty good hand­ball play­er.

Tom is missed greatly by all that knew him.

Steven Lipp­man is Dis­tin­guished Pro­fess­or Emer­it­us (George Rob­bins Chair in Man­age­ment) at UCLA’s An­der­son School of Man­age­ment.