Celebratio Mathematica

It is with sad­ness that we con­firm the passing of Dis­tin­guished Pro­fess­or Emer­it­us in the De­part­ment of Math­em­at­ics Mur­ray Rosen­blatt. He died Wed­nes­day, Oc­to­ber 9, 2019, at the age of 93.

Rosen­blatt was born Septem­ber 7, 1926, and grew up in New York City. He earned his Bach­el­or of Sci­ence de­gree from the City Col­lege of New York in 1946, and sub­sequently pur­sued a PhD in math­em­at­ics at Cor­nell Uni­versity between 1946 and 1949. As a gradu­ate stu­dent, Rosen­blatt took classes from and in­ter­ac­ted with prom­in­ent sci­ent­ists and math­em­aticians, in­clud­ing Richard Feyn­man, Hans Bethe, Philip Mor­ris­on, Wil­li­am Feller, and Mark Kac. The lively Cor­nell prob­ab­il­ity com­munity sur­round­ing Feller and Kac in­cluded re­cent PhDs, Gil­bert Hunt and Kai Lai Chung, and many vis­it­ors such as Joseph Doob and Mon­roe Don­sker. Rosen­blatt’s dis­ser­ta­tion: “On dis­tri­bu­tions of cer­tain Wien­er func­tion­als” was writ­ten un­der the dir­ec­tion of Kac and con­sidered prob­lems re­lated to the now fam­ous Feyn­man–Kac for­mula.

After com­plet­ing his PhD in 1949, Rosen­blatt spent one year at Cor­nell as a postdoc­tor­al fel­low, dur­ing which time he and Adylin (Ady) Lipson mar­ried. The couple moved to Chica­go in 1950 where Rosen­blatt was an in­struct­or and then as­sist­ant pro­fess­or in the “Com­mit­tee on Stat­ist­ics” as it was then called at the Uni­versity of Chica­go. Dur­ing a vis­it of Ulf Gren­ander to Chica­go in 1951–52, he and Rosen­blatt ini­ti­ated a short but highly in­flu­en­tial col­lab­or­a­tion on time series cul­min­at­ing in the book, Stat­ist­ic­al Ana­lys­is of Sta­tion­ary Time Series (Wiley, 1957). This book re­mains a clas­sic today.

Rosen­blatt sub­sequently held ap­point­ments at Columbia Uni­versity, In­di­ana Uni­versity and Brown Uni­versity be­fore join­ing the nas­cent De­part­ment of Math­em­at­ics at the Uni­versity of Cali­for­nia San Diego in 1964. Like oth­er seni­or fac­ulty re­cruited to UC San Diego in the early days of the math­em­at­ics de­part­ment such as Er­rett Bish­op, Ad­ri­ano Gar­sia, and Ron­ald Getoor, Rosen­blatt re­mained at the uni­versity for the rest of his ca­reer. He served as the second de­part­ment chair after the founder Stefan “Steve” Warschawski and helped shape the de­part­ment in­to a first-rate math­em­at­ics de­part­ment. He re­tired from UC San Diego in 1994 and served as pres­id­ent of the Emer­iti As­so­ci­ation in 2003. Rosen­blatt re­mained act­ive in re­search for many years after his re­tire­ment with his last pa­per ap­pear­ing when he was 89.

For much of his ca­reer, Rosen­blatt had an in­terest in ap­plic­a­tions of math­em­at­ics, es­pe­cially in the phys­ic­al and earth sci­ences. He was al­ways eager to dis­cuss math­em­at­ics and sci­ence with col­leagues, even in his fi­nal years. In this spir­it, in 2016, the Mur­ray and Adylin Rosen­blatt En­dowed Lec­ture Series in Ap­plied Math­em­at­ics was ini­ti­ated at UC San Diego fea­tur­ing ex­pos­it­ory lec­tures on math­em­at­ics and stat­ist­ics prob­lems in areas of ap­plic­a­tion.

Rosen­blatt was one of the lead­ing fig­ures in prob­ab­il­ity and stat­ist­ics in the last half of the 20th cen­tury, par­tic­u­larly in the areas of time series, Markov pro­cesses, and non­para­met­ric func­tion es­tim­a­tion. Among his many con­tri­bu­tions, he con­duc­ted sem­in­al work on dens­ity es­tim­a­tion, cent­ral lim­it the­or­ems un­der strong mix­ing con­di­tions, spec­tral do­main meth­ods, and long memory pro­cesses. Dur­ing his long and dis­tin­guished ca­reer, he pub­lished over 150 pa­pers and five books. The Rosen­blatt name has been at­tached to two not­able con­cepts. The Rosen­blatt Trans­form­a­tion, which stems from a 1952 pa­per with the mod­est title, “Re­marks on a mul­tivari­ate trans­form­a­tion,” has be­come a much used pro­ced­ure for test­ing good­ness of fit for mul­tivari­ate dis­tri­bu­tions. In his 1961 pa­per titled, “De­pend­ence and in­de­pend­ence,” Rosen­blatt pro­duced a simple time series with long memory that ex­hib­its a non­cent­ral lim­it the­or­em in that a non-Gaus­si­an dis­tri­bu­tion arises as the lim­it of nor­mal­ized sums of the de­pend­ent ran­dom vari­ables in the series. The lim­it dis­tri­bu­tion has be­come known as the Rosen­blatt dis­tri­bu­tion and re­lated long memory lim­it stochast­ic pro­cesses have been called Rosen­blatt pro­cesses.

Rosen­blatt re­ceived many re­cog­ni­tions for his out­stand­ing re­search. He was a Fel­low of the Amer­ic­an As­so­ci­ation for the Ad­vance­ment of Sci­ence, the Amer­ic­an Math­em­at­ic­al So­ci­ety, the In­sti­tute of Math­em­at­ic­al Stat­ist­ics, the So­ci­ety for In­dus­tri­al and Ap­plied Math­em­at­ics, a Gug­gen­heim Fel­low, an Over­seas Fel­low of Churchill Col­lege, Cam­bridge UK, and was elec­ted as a mem­ber of the Na­tion­al Academy of Sci­ences. In 1970 he de­livered the Wald Lec­tures, the most pres­ti­gi­ous lec­ture series of the In­sti­tute of Math­em­at­ic­al Stat­ist­ics.

Twenty-two stu­dents earned their PhDs un­der Rosen­blatt’s dir­ec­tion — 14 of them were at UC San Diego — and many went on to suc­cess­ful aca­dem­ic ca­reers. One of his former stu­dents, Richard Dav­is, now pro­fess­or of stat­ist­ics at Columbia Uni­versity, re­called re­cently, “He was there for his stu­dents with great en­cour­age­ment and sup­port. To­geth­er, Mur­ray and Ady served as sur­rog­ate par­ents to many of Mur­ray’s stu­dents.” Sadly, Ady passed away in 2009. Rosen­blatt is sur­vived by his daugh­ter, Karin Rosen­blatt of Cham­paign, Ill., and his son, Daniel Rosen­blatt of Live Oak, Tex.

Steven Boggs, who holds the Chan­cel­lor’s Chair in Phys­ics, serves as the Dean of Phys­ic­al Sci­ences at the Uni­versity of Cali­for­nia, San Diego.

Lei Ni, a mem­ber of the De­part­ment of Math­em­at­ics at the Uni­versity of Cali­for­nia, San Diego, was serving as Chair­man of that de­part­ment at the time of the ob­it­u­ary’s pub­lic­a­tion.