Celebratio Mathematica

Kai Lai Chung, a lead­ing prob­ab­il­ist of the second half of the 20th cen­tury, was born in 1917 in Shang­hai, China, to a fam­ily with roots in Hang­zhou in Zheji­ang Province. He entered Tsinghua Uni­versity in 1936; he first stud­ied phys­ics but gradu­ated in math­em­at­ics in 1940. Dur­ing the war with Ja­pan, sev­er­al ma­jor uni­versit­ies in the Beijing–Tianjin re­gion moved to the south­w­est city of Kun­ming and re­grouped as the Na­tion­al South­west­ern As­so­ci­ated Uni­versity. While there, Chung worked in a po­s­i­tion ana­log­ous to that of as­sist­ant pro­fess­or. He first star­ted do­ing re­search in num­ber the­ory with the num­ber the­or­ist Lo-Keng Hua, and then switched to prob­ab­il­ity the­ory with the math­em­at­ic­al stat­ist­i­cian Pao-Lu Hsu.

In 1944, Kai Lai Chung won a highly com­pet­it­ive Box­er Re­bel­lion In­dem­nity schol­ar­ship for study in the United States, and ar­rived at Prin­ceton Uni­versity in Decem­ber 1945. He com­pleted his Ph.D. thes­is in 1947 un­der the su­per­vi­sion of the Swedish stat­ist­i­cian Har­ald Cramér, who was vis­it­ing Prin­ceton at the time. Chung’s thes­is was titled On the max­im­um par­tial sum of se­quences of in­de­pend­ent ran­dom vari­ables [1]; in it he proved the fam­ous Chung’s law of the it­er­ated log­ar­ithm. Sub­sequently, he held aca­dem­ic ap­point­ments at the Uni­versity of Chica­go, Columbia Uni­versity, Uni­versity of Cali­for­nia at Berke­ley, Cor­nell Uni­versity, and Syra­cuse Uni­versity. He joined Stan­ford Uni­versity in 1961 and re­mained there un­til his re­tire­ment in 1988.

Over the years, Kai Lai Chung held ex­ten­ded vis­it­ing ap­point­ments at sev­er­al in­sti­tu­tions, among them Uni­versity of Stras­bourg (France), Uni­versity of Pisa (Italy), and the ETH (Ei­dgenöss­is­che Tech­nis­che Hoch­schule) of Zurich (Switzer­land). He was a George A. Miller Vis­it­ing Pro­fess­or at the Uni­versity of Illinois at Urb­ana–Cham­paign in 1970–71, and a Fel­low of the In­sti­tute of Math­em­at­ic­al Stat­ist­ics. In 1976 he was made an Over­seas Fel­low of Churchill Col­lege of the Uni­versity of Cam­bridge.

Kai Lai Chung was a highly in­nov­at­ive math­em­atician, and his re­search had a ma­jor in­flu­ence on sev­er­al areas in prob­ab­il­ity: sums of in­de­pend­ent ran­dom vari­ables, Markov chains in con­tinu­ous time and es­pe­cially their bound­ary the­ory, time re­versal of Markov pro­cesses, prob­ab­il­ist­ic po­ten­tial the­ory, Browni­an ex­cur­sions, and gauge the­or­ems for the Schrödinger equa­tion. He au­thored 133 journ­al art­icles span­ning a peri­od of 70 years. A se­lec­tion of his works was pub­lished in 2008 by World Sci­entif­ic in cel­eb­ra­tion of his 90th birth­day. In ad­di­tion to his re­search art­icles, Chung’s el­ev­en books have in­flu­enced sev­er­al gen­er­a­tions of stu­dents of prob­ab­il­ity, both at the gradu­ate and un­der­gradu­ate levels. He was well known for his el­eg­ant and lively prose, as well as for his clear and pre­cise ex­pos­i­tion. His widely used gradu­ate text, A Course in Prob­ab­il­ity The­ory [2], first pub­lished in the late 1960s, is now in its third edi­tion, and his pop­u­lar un­der­gradu­ate text, Ele­ment­ary Prob­ab­il­ity with Stochast­ic Pro­cesses [3], cur­rently in its fourth edi­tion (with Farid Ait­Sah­lia as coau­thor), has been trans­lated in­to many lan­guages, in­clud­ing Eng­lish, Chinese, Ger­man, Per­sian, Rus­si­an and Span­ish.

Kai Lai Chung taught prob­ab­il­ity for nearly 40 years and su­per­vised 15 Ph.D. stu­dents. The Math­em­at­ics Gene­a­logy Pro­ject cur­rently lists a total of 142 aca­dem­ic des­cend­ants. His en­thu­si­asm for math­em­at­ics was evid­ent in his en­er­get­ic classroom and re­search present­a­tions and in his lively, spir­ited and can­did one-on-one dis­cus­sions. He is par­tic­u­larly re­membered by col­lab­or­at­ors and col­leagues for stim­u­lat­ing ques­tions, de­livered in per­son, by let­ter, over the phone and, in later years, by fax.

In 1981, Kai Lai Chung, along with Er­han Çin­lar and Ron­ald Getoor, ini­ti­ated the Sem­inars on Stochast­ic Pro­cesses. These meet­ings, with their in­nov­at­ive struc­ture of just a few form­al talks, al­low­ing plenty of time for in­form­al dis­cus­sions and re­search prob­lem ses­sions, have con­tin­ued as highly suc­cess­ful an­nu­al con­fer­ences to this day. The 1987 Sem­in­ar, held at Prin­ceton Uni­versity, honored Kai Lai Chung and Gil­bert Hunt around the time of their re­tire­ments. Among the oth­er par­ti­cipants were Claude Del­lacher­ie, Paul-An­dré Mey­er, and Jacques Neveu, who came from France to hon­or Chung and Hunt, and also to tell of their re­spect­ive in­flu­ences on the French school of prob­ab­il­ity. The 2010 Sem­in­ar, hos­ted by the Uni­versity of Cent­ral Flor­ida on March 11–13 of that year, had a spe­cial ses­sion to com­mem­or­ate Kai Lai Chung’s con­tri­bu­tions to prob­ab­il­ity.

Kai Lai Chung also played an in­flu­en­tial role in the de­vel­op­ment of mod­ern prob­ab­il­ity the­ory in his nat­ive China im­me­di­ately after the chaot­ic years of the Cul­tur­al Re­volu­tion (1966–1976). His vis­it to China in 1979 (to­geth­er with Joseph Doob and Jacques Neveu) was the start­ing point for re­newed con­tact of Chinese prob­ab­il­ists with the West. He vis­ited China many times there­after, giv­ing nu­mer­ous lec­tures and short courses, and helped young Chinese stu­dents gain op­por­tun­it­ies to study in the United States. A con­fer­ence, titled From Markov Pro­cesses to Browni­an Mo­tion and Bey­ond, was held at Pek­ing Uni­versity on June 13–16, 2010, to hon­or the memory of Kai Lai Chung and his con­tri­bu­tion to the de­vel­op­ment of mod­ern prob­ab­il­ity the­ory in China.

Kai Lai Chung’s zest for life, com­bined with his en­er­get­ic curi­os­ity, was ap­par­ent to all who knew him. Be­sides pur­su­ing math­em­at­ics, he also had a broad range of cul­tur­al in­terests. Edu­cated in a clas­sic­al Chinese tra­di­tion in his youth, Kai Lai Chung was deeply fa­mil­i­ar with the Chinese lit­er­ary her­it­age and forms of the Chinese lan­guage. His fam­ily re­calls how, in his many travels to China from 1979 on­wards, fol­low­ing the open­ing of dip­lo­mat­ic re­la­tions between China and the United States, he sought out and helped re-es­tab­lish the stature of many writers, po­ets, paint­ers, and cal­li­graph­ers he coun­ted as old friends. His pas­sion for cul­ture was not re­stric­ted to that of his home­land. He traveled ex­tens­ively, mak­ing the ac­quaint­ance of many math­em­aticians around the world. He was an avid hiker and walk­er, and while trav­el­ing al­ways made sure to vis­it im­port­ant his­tor­ic­al, cul­tur­al, or nat­ur­al sites. He sur­prised many with his wide-ran­ging and in­tim­ate know­ledge of lit­er­at­ure, his­tory, and mu­sic, es­pe­cially op­era. He spoke sev­er­al lan­guages and prac­ticed them with the many vis­it­ors who came to see him at Stan­ford from France, Ger­many, Italy, Rus­sia, and oth­er coun­tries over the years. In his later years, he taught him­self Itali­an in re­tire­ment and pub­lished a math­em­at­ic­al pa­per in that lan­guage.

Kai Lai Chung passed away on June 1, 2009, at the age of 91.