Rick Durrett

Richard Timothy Durrett
Education	Emory University Stanford University
Scientific career
Fields	Statistics Mathematics
Workplaces	UCLA Cornell University Duke University
Thesis	Conditioned Limit Theorems for Some Null Recurrent Markov Processes (1976)
Doctoral advisor	Donald Iglehart
Doctoral students	Claudia Neuhauser

Richard Timothy Durrett (born 1951) is an American mathematician whose research concerns probability theory, stochastic processes, and their applications to mathematical biology, including population genetics, ecology, epidemiology, and cancer modeling. He is the James B. Duke Emeritus Professor of Mathematics at Duke University, having previously held faculty positions at the University of California, Los Angeles (UCLA) and Cornell University.

Durrett was elected to the United States National Academy of Sciences in 2007 and to the American Academy of Arts and Sciences in 2002. He is also a fellow of the American Mathematical Society, the Institute of Mathematical Statistics, and the American Association for the Advancement of Science. His textbook Probability: Theory and Examples was described in a review for the Mathematical Association of America as one of the two most popular graduate-level texts on probability, alongside Billingsley's Probability and Measure.

Education

Durrett received his Bachelor of Science (1972) and Master of Science (1973) degrees in mathematics from Emory University. He then entered the Operations Research program at Stanford University, where he completed his Ph.D. in 1976 under the supervision of Donald Iglehart. His doctoral dissertation, titled Conditioned Limit Theorems for Some Null Recurrent Markov Processes, appeared in the Annals of Probability in 1976.

Durrett has said that he initially enrolled at Emory as a pre-medical student during the Vietnam War era but switched to mathematics after finding the laboratory component of pre-med unappealing, while still wanting to apply mathematics to real-world problems; this led him to operations research at Stanford.

Career

Durrett began his academic career at the University of California, Los Angeles (UCLA) in 1976 as an E. R. Hedrick Assistant Professor and was promoted through the ranks to full professor, remaining at UCLA until 1985. In 1985 he joined the faculty of Cornell University, where he remained for 25 years.

In 2010 Durrett moved to Duke University as the James B. Duke Professor of Mathematics, a position he held until his retirement in 2023, simultaneously serving as associate director of the Statistical and Applied Mathematical Sciences Institute (SAMSI) in the Research Triangle from 2010. He was drawn to Duke partly by the milder climate of North Carolina and partly by the opportunities for collaboration with biostatisticians, computational biologists, and applied mathematicians at Duke, the University of North Carolina at Chapel Hill, and North Carolina State University. Upon retirement he became the James B. Duke Emeritus Professor of Mathematics.

Durrett has supervised more than fifty doctoral students, including Rodrigo Bañuelos (UCLA, 1984), Claudia Neuhauser (Cornell, 1990), Nathaniel Berestycki (Cornell, 2005), Daniel Remenik (Cornell, 2009), and Shirshendu Chatterjee (Duke, 2011). He has also mentored postdoctoral fellows including Vlada Limic, Lea Popovic, Soumik Pal, Jon Peterson, David Sivakoff, and Matt Junge.

He served as an editor of the Annals of Applied Probability from 1997 to 1999 and has been involved in organizing numerous conferences, including the Southeastern Probability Conference, the Workshop for Women in Probability, and programs at the Mathematical Biosciences Institute and the Banff International Research Station (BIRS).

Research

Durrett's research spans probability theory and its applications. His early work focused on interacting particle systems, percolation theory, and contact processes, building on the frameworks developed by Thomas M. Liggett and Frank Spitzer. His 1980 paper with T. M. Liggett determined the shape of the limit set in Richardson's model for the spread of an infection.

Stochastic spatial models in ecology

In the late 1980s Durrett began a long-running collaboration with the ecologist Simon Levin of Princeton University on stochastic spatial models in ecology. Their 1994 paper The Importance of Being Discrete (and Spatial) argued that spatial structure can qualitatively change the dynamics of ecological interactions and is among the most cited papers in mathematical ecology. Their subsequent papers studied species–area curves, allelopathy, interspecific competition, and the spread of epidemics using interacting particle systems and stochastic spatial models.

Population genetics and cancer

Beginning in the late 1990s Durrett turned to population genetics, working with C. F. Aquadro and others on the evolutionary dynamics of microsatellite repeat length distributions and, with Jason Schweinsberg, on approximating selective sweeps by random partitions. His 2008 paper with Deena Schmidt, Waiting for two mutations, studied the limits of Darwinian evolution in regulatory sequence evolution.

Durrett's later research has applied branching processes and stochastic models to cancer biology, including models of tumor heterogeneity, the evolution of resistance to therapy, and the dynamics of clonal expansion.

Random graphs

A third strand of Durrett's work concerns stochastic processes on random graphs. He showed, with Shirshendu Chatterjee, that contact processes on random graphs with power-law degree distributions have critical value zero—meaning infection can survive for any positive infection rate. His 2010 Inaugural Article as a member of the National Academy of Sciences, published in the Proceedings of the National Academy of Sciences, examined the spread of epidemics and opinions on random graphs. This work is collected in part in his monograph Random Graph Dynamics (Cambridge University Press, 2007; second edition Springer, 2025).

Honors and awards

Durrett has received a number of honors recognizing his contributions to probability theory and mathematical biology. He was awarded a Sloan Research Fellowship from the Alfred P. Sloan Memorial Foundation for 1981–1983, and an AMS Centennial Fellowship for 1984–1986. In 1981 he was elected a fellow of the Institute of Mathematical Statistics. He received a Guggenheim Fellowship for 1988–1989.

In 1990 he delivered a 45-minute invited lecture at the International Congress of Mathematicians in Kyoto. He gave the Coxeter Lectures at the Fields Institute in 1999 and the IMS Wald Lectures at the World Congress of Probability and Statistics in Singapore in 2008.

Durrett was elected to the American Academy of Arts and Sciences in 2002 and to the United States National Academy of Sciences in 2007. He was elected a fellow of the American Association for the Advancement of Science in 2009 and was named a fellow of the American Mathematical Society in the inaugural class of 2012.

Selected publications

Books

• Durrett, R. (1984). Brownian Motion and Martingales in Analysis. Wadsworth Publishing. ISBN 978-0-534-03065-0.
• Durrett, R. (1988). Lecture Notes on Particle Systems and Percolation. Wadsworth Publishing. ISBN 978-0-534-09478-2.
• Durrett, R. (2019). Probability: Theory and Examples. Cambridge Series in Statistical and Probabilistic Mathematics (5th ed.). Cambridge University Press. ISBN 978-1-108-47368-2.
• Durrett, R. (2008). Probability Models for DNA Sequence Evolution (2nd ed.). Springer. ISBN 978-0-387-78168-6.
• Durrett, R. (2007). Random Graph Dynamics. Cambridge University Press. ISBN 978-0-521-86656-9.
• Durrett, R. (2016). Essentials of Stochastic Processes (3rd ed.). Springer. ISBN 978-3-319-45613-3.
• Durrett, R. (2009). Elementary Probability for Applications. Cambridge University Press. ISBN 978-0-521-86756-6.
• Durrett, R. (2015). Branching Process Models of Cancer. Springer. ISBN 978-3-319-16064-1.

Selected research papers

• Durrett, R.; Resnick, S. I. (1978). "Functional limit theorems for dependent variables". The Annals of Probability. 6 (5): 829–846. doi:10.1214/aop/1176995325. ISSN 0091-1798.
• Cox, J. T.; Durrett, R. (1981). "Some limit theorems for percolation processes with necessary and sufficient conditions". The Annals of Probability. 9 (4): 583–603. doi:10.1214/aop/1176994365. ISSN 0091-1798.
• Durrett, R. (1984). "Oriented percolation in two dimensions". The Annals of Probability. 12 (4): 999–1040. doi:10.1214/aop/1176993160. ISSN 0091-1798.
• Durrett, R.; Liggett, T. M. (1983). "Fixed points of the smoothing transformation". Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 64 (3): 275–301. doi:10.1007/BF00535706. ISSN 0044-3719.
• Durrett, R.; Levin, S. (1994). "The importance of being discrete (and spatial)". Theoretical Population Biology. 46 (3): 363–394. Bibcode:1994TPBio..46..363D. doi:10.1006/tpbi.1994.1032. ISSN 0040-5809.
• Durrett, R.; Neuhauser, C. (1994). "Particle systems and reaction-diffusion equations". The Annals of Probability. 22 (1): 289–333. doi:10.1214/aop/1176988855. ISSN 0091-1798.
• Kruglyak, S.; Durrett, R.; Schug, M.; Aquadro, C. (1998). "Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations". Proceedings of the National Academy of Sciences. 95 (18): 10774–10778. doi:10.1073/pnas.95.18.10774. ISSN 0027-8424. PMC 27948. PMID 9724780.
• Durrett, R.; Schweinsberg, J. (2008). "Waiting for two mutations: with applications to regulatory sequence evolution and the limits of Darwinian evolution". Genetics. 180 (1): 1501–1509. doi:10.1534/genetics.107.082971. ISSN 0016-6731. PMC 2535691. PMID 18791261.
• Chatterjee, S.; Durrett, R. (2009). "Contact processes on random graphs with power law degree distributions have critical value zero". The Annals of Probability. 37 (6): 2332–2356. doi:10.1214/09-AOP471. ISSN 0091-1798.
• Durrett, R. (2009). "Coexistence in stochastic spatial models". The Annals of Applied Probability. 19 (2): 477–496. doi:10.1214/08-AAP566. ISSN 1050-5164.
• Durrett, R. (2010). "Some features of the spread of epidemics and opinions on a random graph". Proceedings of the National Academy of Sciences. 107 (10): 4491–4498. doi:10.1073/pnas.0911198107. ISSN 0027-8424. PMC 2842029. PMID 20160135.

External links

• Official website
• Richard Timothy Durrett at the Mathematics Genealogy Project
• Rick Durrett publications indexed by Google Scholar
• Profile at the Simons Institute for the Theory of Computing