• Department of Mathematics
• University of California
• Los Angeles CA 90095-1555

• (310) 825-1339

• tml@math.ucla.edu

Education

• A.B. in Mathematics, Oberlin College 1965.
• M.S. in Mathematics, Stanford University, 1966.
• Ph.D. in Mathematics, Stanford University, 1969.

Main interests

• Probability Theory; Interacting Particle Systems

Positions Held

• Assistant Professor of Mathematics, UCLA, 1969-1973
• Associate Professor of Mathematics, UCLA, 1973-1976.
• Professor of Mathematics, UCLA, 1976-present.
• Vice Chair for Administration, Mathematics Department, UCLA, 1978-1981.
• Chair, Mathematics Department, UCLA, 1991-1994.
• Associate Editor of the Annals of Probability, 1979-1984.
• Editor of the Annals of Probability, 1985-1987.
• Associate Editor of Stochastic Processes and their Applications, 1993-1999.
• Undergraduate Vice Chair, Mathematics Department, UCLA, 2004-2006.

Honors

• Alfred P. Sloan Research Fellowship, 1973-1977.
• Elected Fellow of the Institute of Mathematical Statistics, 1976.
• Invited speaker at the 1986 International Congress of Mathematicians.
• IMS Wald Memorial Lecturer, 1996.
• Guggenheim Fellowship, 1997-1998.

Ph.D. Students

• Norman Matloff, 1974 (UC Davis)
• Diane Schwartz, 1974 (CSU Northridge)
• Enrique Andjel, 1981 (U. Provence, Marseille, France)
• Dayue Chen , 1989 (Peking University)
• Xijian Liu, 1991 (US Census Bureau)
• Shirin Handjani, 1993 (San Diego)
• Amber Puha, 1998 (CSU San Marcos)
• Paul Jung, 2003 (Cornell)

Thomas M. Liggett, Clustering and coexistence in threshold voter models,in "Cellular Automata and Cooperative Systems", Kluwer, 1993, pp. 403-410.

Thomas M. Liggett, Coexistence in threshold voter models, Ann. Probab. 22 (1994), 764-802.

Jon Aaronson, Thomas M. Liggett and Pierre Picco, Equivalence of renewal sequences and isomorphism of random walks, Israel J. Math. 87 (1994), 65-76.

Thomas M. Liggett, Survival and coexistence in interacting particle systems, in "Probability and Phase Transition", Kluwer, 1994, pp. 209-226.

Thomas M. Liggett and Peter Petersen, The law of large numbers and the square root of 2, Amer. Math Monthly 102 (1995), 31-35.

Thomas M. Liggett, Improved upper bounds for the contact process critical value, Ann. Probab. 23 (1995), 697-723.

Pablo A. Ferrari, Antonio Galves and Thomas M. Liggett, Exponential waiting time for filling a large interval in the symmetric simple exclusion process, Annales de L'Institut Henri Poincaré 31 (1995), 155-175.

Thomas M. Liggett, Survival of discrete time growth models, with applications to oriented percolation, Ann. Appl. Probab. 5 (1995), 613-636.

Thomas M. Liggett, Multiple transition points for the contact process on the binary tree. Ann. Probab. 24 (1996), 1675-1710.

Thomas M. Liggett, Roberto H. Schonmann and Alan M. Stacey, Domination by product measures. Ann. Probab. 25 (1997), 71-95.

Thomas M. Liggett, Branching random walks and contact processes on homogeneous trees. Probab. Th. Rel. Fields 106 (1996), 495-519.

Thomas M. Liggett, The 1996 Wald Memorial Lectures: Stochastic models of interacting systems. Ann. Probab. 25 (1997), 1-29.

Vladimir Belitsky, Pablo A. Ferrari, Norio Konno and Thomas M. Liggett, A strong correlation inequality for contact processes and oriented percolation. Stoch. Proc. Appl.67 (1997), 213-225.

Thomas M. Liggett, Ultra logconcave sequences and negative dependence. J. Comb. Th. A. 79 (1997), 315-325.

Thomas M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Grund. fur Math. Wissen., Vol 324, Springer (1999).

Thomas M. Liggett, Branching random walks on finite trees. Perplexing Problems in Probability: Festschrift in Honor of Harry Kesten. Birkhauser Progress in Probability Series (1999), 315-330.

Thomas M. Liggett, Monotonicity of conditional distributions and growth models on trees. Ann. Probab. 28, (2000), 1645-1665.

Thomas M. Liggett, Tagged particle distributions, or How to choose a head at random. In and Out of Equilibrium: Probability with a Physics Flavor. Birkhauser Progress in Probability Series (2002), 133-162.

Alexander E. Holroyd and Thomas M. Liggett, How to find an extra head: optimal random shifts of Bernoulli and Poisson random fields. Ann. Probab. 29 (2001), 1405-1425.

Maury Bramson, Thomas M. Liggett and Thomas Mountford, Characterization of stationary measures for one dimensional exclusion processes. Ann. Probab. 30 (2002), 1529-1575.

Thomas M. Liggett, Interacting Particle Systems -- An Introduction. Lectures given at the School and Conference on Probability Theory at the International Center for Theoretical Physics, Trieste, May 13-17, 2002.

Phillip Bonacich and Thomas M. Liggett, Asymptotics of a matrix valued Markov chain arising in sociology. Stoch. Proc. Appl. 104 (2003), 155-171.

Thomas M. Liggett, Negative correlations and particle systems. Markov Proc. Rel. Fields 8 (2002), 547-564.

Alexander E. Holroyd, Thomas M. Liggett and Dan Romik, Integrals, partitions and cellular automata. Trans. A. M. S. 356 (2004), 3349-3368

Richard Arratia and Thomas M. Liggett, How likely is an i.i.d. degree sequence to be graphical? Annals of Applied Probability 15 (2005), 652-670.

Thomas M. Liggett and Silke W. W. Rolles, An infinite stochastic model of social network formation. Stoch. Proc. Appl. 113 (2004), 65-80.

Maury Bramson and Thomas M. Liggett, Exclusion processes in higher dimensions: stationary measures and convergence. Ann. Probab. 33 (2005), 2255-2313.

Thomas M. Liggett and Jeffery E. Steif, Stochastic domination: The contact process, Ising models and FKG measures. Ann. Inst. H. Poincare Probab. Statist. 42 (2006), 223-243.

Thomas M. Liggett, Conditional association and spin systems. ALEA - Latin American Journal of Probability and Mathematical Statistics 1 (2006), 1-19.

Thomas M. Liggett, Jeffery E. Steif and Balint Toth, Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete moment problem. Ann. Probab.

Thomas M. Liggett, Steven A. Lippman and Richard P. Rumelt, The asymptotic Shapley value for a simple market game.

Lincoln Chayes and Thomas M. Liggett, One dimensional nearest neighbor exclusion processes in inhomogeneous and random environments. J. Stat. Phys.

Thomas M. Liggett, Rinaldo B. Schinazi and Jason Schweinsberg, A contact process with mutations on a tree.

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