Thomas M. Liggett

How To Reach Me Mailing Address: Department of Mathematics University of California Los Angeles CA 90095-1555 Telephone: (310) 825-1339 Email: tml@math.ucla.edu

• Mathematics 275C - Spring 2008
• Mathematics 131AH - Fall 2007
• Mathematics 275A - Fall 2007
• Mathematics 131BH - Winter 2008
• Mathematics 170A - Winter 2007
• Mathematics 275B - Winter 2007
• Mathematics 275E and 285K/2 - Winter and Spring 2006
• Mathematics 171 - Spring 2005
• Mathematics 31B - Fall 2004
• Mathematics 170A - Spring 2004
• Mathematics 170B - Winter 2004
• Mathematics 131C - Spring 2003
• Mathematics 131B - Spring 2001
• Mathematics 33B - Winter 2001
• Mathematics 131A - Winter 2001

• My 1985 book "Interacting Particle Systems" has been reprinted by Springer in its series "Classics in Mathematics". By going to the Springer web page, you can find some reviews and order the book. For a list of typos in the original printing, click here
• UCLA Probability Seminar
• UCLA Probability & Mathematical Physics Group
• Additions and corrections for my 1999 book "Stochastic Interacting Systems: Contact, Voter and Exclusion Processes".
• Shorter CV

Education

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

Mathematical Geneology

• S. Karlin, S. Bochner, E. Schmidt, D. Hilbert, C. Lindeman, F. Klein, R. Lipschitz, G. Dirichlet, S. Poisson and J. Fourier, J. Lagrange, L. Euler, J. Bernoulli.

Research Areas

• 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.
• Member, National Academy of Sciences, 2008-.

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 (Susquehanna International Group, Philadelphia)

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. 35 (2007), 867-914.

Thomas M. Liggett, Steven A. Lippman and Richard P. Rumelt, The asymptotic Shapley value for a simple market game. Economic Theory (2008).

Lincoln Chayes and Thomas M. Liggett, One dimensional nearest neighbor exclusion processes in inhomogeneous and random environments. J. Stat. Phys. 129 (2007), 193-203.

Thomas M. Liggett, Rinaldo B. Schinazi and Jason Schweinsberg, A contact process with mutations on a tree. Stoch. Proc. Appl. 118 (2008), 319-332.

Julius Borcea, Petter Branden and Thomas M. Liggett, Negative dependence and the geometry of polynomials. J. American Mathematical Society.

Thomas M. Liggett, Distributional limits for the symmetric exclusion process. Stoch. Proc. Appl.

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