Thomas M. Liggett | Academic Influence

Thomas M. Liggett's AcademicInfluence.com Rankings

Thomas M. Liggett

Mathematics

#2467

World Rank

#3809

Historical Rank

#974

USA Rank

Measure Theory

#1082

World Rank

#1394

Historical Rank

#396

USA Rank

mathematics Degrees

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Mathematics

Thomas M. Liggett's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Thomas M. Liggett Influential?

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According to Wikipedia, Thomas Milton Liggett was a mathematician at the University of California, Los Angeles. He worked in probability theory, specializing in interacting particle systems. Early life Thomas Milton Liggett was born on March 29, 1944, in Danville, Kentucky. Liggett moved at the age of two with his missionary parents to Latin America, where he was educated in Bueno Aires, Argentina and San Juan, Puerto Rico. He graduated from Oberlin College with a Bachelor of Arts in 1965, where he was influenced towards probability by Samuel Goldberg , an ex-student of William Feller. He moved to Stanford, taking classes with Kai Lai Chung, and writing his thesis, Weak Convergence of Conditioned Sums of Independent Random Vectors, in 1969 with advisor Samuel Karlin on problems associated with the invariance principle. He graduated with a Master of Science in 1966 and a Doctor of Philosophy in 1969.

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Thomas M. Liggett's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Interacting Particle Systems (1985) (2194)
Stochastic Interacting Systems: Contact, Voter and Exclusion Processes (1999) (1525)
Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model (1975) (975)
GENERATION OF SEMI-GROUPS OF NONLINEAR TRANSFORMATIONS ON GENERAL BANACH SPACES, (1971) (871)
Domination by product measures (1997) (424)
Fixed points of the smoothing transformation (1983) (262)
Negative dependence and the geometry of polynomials (2007) (253)
An Improved Subadditive Ergodic Theorem (1985) (215)
Continuous Time Markov Processes: An Introduction (2010) (185)
Stochastic Games with Perfect Information and Time Average Payoff (1969) (156)
Coupling the Simple Exclusion Process (1976) (142)
The Shape of the Limit Set in Richardson's Growth Model (1981) (138)
Existence theorems for infinite particle systems (1972) (108)
Proof of Aldous' spectral gap conjecture (2009) (107)
Generalized potlatch and smoothing processes (1981) (103)
Ergodic theorems for coupled random walks and other systems with locally interacting components (1981) (102)
Ergodic theorems for the asymmetric simple exclusion process (1975) (98)
Shocks in the asymmetric exclusion process (1988) (90)
Optimal Stopping for Partial Sums (1972) (82)
Multiple transition points for the contact process on the binary tree (1996) (76)
The survival of contact processes (1978) (74)
Integrals, partitions, and cellular automata (2003) (67)
Ultra Logconcave Sequences and Negative Dependence (1997) (66)
The stochastic evolution of infinite systems of interacting particles (1977) (66)
$L_2$ Rates of Convergence for Attractive Reversible Nearest Particle Systems: The Critical Case (1991) (63)
Survival of Discrete Time Growth Models, with Applications to Oriented Percolation (1995) (60)
An Infinite Particle System with Zero Range Interactions (1973) (57)
Stochastic models of interacting systems (1997) (57)
Coexistence in Threshold Voter Models (1994) (56)
A characterization of the invariant measures for an infinite particle system with interactions (1973) (54)
Random invariant measures for Markov chains, and independent particle systems (1978) (50)
An Invariance Principle for Conditioned Sums of Independent Random Variables (1968) (49)
Exponential $L_2$ Convergence of Attractive Reversible Nearest Particle Systems (1989) (49)
The Survival of One-Dimensional Contact Processes in Random Environments (1992) (48)
Critical Phenomena for Spitzer's Reversible Nearest Particle Systems (1982) (45)
Improved Upper Bounds for the Contact Process Critical Value (1995) (43)
Tagged Particle Distributions or How to Choose a Head at Random (2002) (40)
Stochastic domination: the contact process, Ising models and FKG measures (2005) (39)
Branching random walks and contact processes on homogeneous trees (1996) (38)
How to Find an extra Head: Optimal Random Shifts of Bernoulli and Poisson Random Fields (2001) (35)
Long Range Exclusion Processes (1980) (31)
Ergodic Theorems for the Asymmetric Simple Exclusion Process II (1977) (31)
Asymptotics of a matrix valued Markov chain arising in sociology (2003) (28)
Stochastic models for large interacting systems and related correlation inequalities (2010) (25)
Interacting Markov Processes (1980) (24)
FINITELY DEPENDENT COLORING (2014) (24)
Clustering in one-dimensional threshold voter models (1992) (24)
How likely is an i.i.d. degree sequence to be graphical (2005) (23)
Attractive Nearest Neighbor Spin Systems on the Integers (1978) (23)
A theorem and a counterexample in the theory of semigroups of nonlinear transformations (1971) (23)
Ergodicity of reversible reaction diffusion processes (1990) (21)
Spatially Inhomogeneous Contact Processes (1991) (20)
Characterization of stationary measures for one-dimensional exclusion processes (2002) (20)
The asymptotic shapley value for a simple market game (2009) (18)
Attractive Nearest Particle Systems (1983) (17)
A Stochastic Model for Phylogenetic Trees (2009) (16)
Negative Correlations And Particle Systems (2002) (15)
Distributional limits for the symmetric exclusion process (2007) (15)
Percolation of arbitrary words in one dimension (2008) (14)
An infinite stochastic model of social network formation (2004) (14)
Monotonicity of conditional distributions and growth models on trees (2000) (13)
Exclusion processes in higher dimensions: Stationary measures and convergence (2005) (13)
Total Positivity and Renewal Theory (1989) (13)
Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem (2005) (12)
SURVIVAL AND COEXISTENCE IN INTERACTING PARTICLE SYSTEMS (1994) (12)
Symmetric 1-Dependent Colorings of the Integers (2014) (12)
Multivariate CLT follows from strong Rayleigh property (2016) (12)
Branching Random Walks on Finite Trees (1999) (11)
One Dimensional Nearest Neighbor Exclusion Processes in Inhomogeneous and Random Environments (2007) (11)
The Periodic Threshold Contact Process (1991) (10)
Systems of independent Markov chains (1987) (10)
The contact process with fast voting (2014) (10)
Convergence to Total Occupancy in an Infinite Particle System with Interactions (1974) (10)
WEAK CONVERGENCE OF CONDITIONED SUMS OF INDEPENDENT RANDOM VECTORS (1970) (8)
Exponential waiting time for filling a large interval in the symmetric simple exclusion process (1995) (8)
A strong correlation inequality for contact processes and oriented percolation (1997) (8)
Scale-free and power law distributions via fixed points and convergence of (thinning and conditioning) transformations (2013) (7)
Conditional Association and Spin Systems (2005) (7)
A contact process with mutations on a tree (2006) (7)
T. E. Harris’ contributions to interacting particle systems and percolation (2011) (7)
On Convergent Diffusions: The Densities and the Conditioned Processes (1970) (7)
Applications of the Dirichlet Principle to finite reversible nearest particle systems (1987) (6)
Seminar on Stochastic Processes, 1991 (1992) (6)
Extensions of the Erdös-Ko-Rado Theorem and a Statistical Application (1977) (6)
A recursive proof of Aldous' spectral gap conjecture (2009) (5)
Reversible Growth Models on Zd: Some Examples (1987) (5)
Finite Reversible Nearest Particle Systems in Inhomogeneous and Random Environments (1992) (5)
Two Critical Exponents for Finite Reversible Nearest Particle Systems (1983) (4)
A recursive approach for Aldous' spectral gap conjecture (2009) (4)
Background and Tools (1999) (4)
Convergence of Sums of Random Variables Conditioned on a Future Change of Sign (1970) (4)
Equivalence of renewal sequences and isomorphism of random walks (1994) (4)
Nearest particle systems: Results and open problems (1986) (4)
Interacting Particle Systems at Saint-Flour (2011) (3)
Finite nearest particle systems (1984) (3)
THE LAW OF LARGE NUMBERS AND 2 (1995) (3)
Stability on {0, 1, 2, …}S: Birth-Death Chains and Particle Systems (2010) (2)
Stochastic Ising Models (2005) (2)
One-dimensional Brownian motion (2010) (2)
Clustering and Coexistence in Threshold Voter Models (1993) (2)
Nearest-Particle Systems (1985) (2)
Survival of the Contact + Voter Process on the Integers (2013) (2)
Asymptotics Of A Matrix Valued Markov Chain (2002) (1)
The Voter Model (2005) (1)
Multi-dimensional Brownian motion and the Dirichlet problem (2010) (0)
The Contact Process (2005) (0)
The Exclusion Process (1985) (0)
PERCOLATION AND INTERACTING SYSTEMS (2012) (0)
Correction: “Coexistence in threshold voter models” [Ann. Probab. 22 (1994), no. 2, 764–802; MR 95m:60164] (1999) (0)
Abstract of the Dissertation Understanding Probabilistic Models Through Limit Theorems (2017) (0)
Lectures in probability, Nagoya 1986 (1987) (0)
PR ] 1 9 D ec 2 00 6 A contact process with mutations on a tree by (2022) (0)
PR ] 1 4 M ay 2 00 9 A stochastic model for phylogenetic trees by (2009) (0)
CHARACTERIZATION OF STATIONARY MEASURESFOR ONE DIMENSIONAL EXCLUSION (2007) (0)
Random Systems with Locally Interacting Objects (1980) (0)
Some Basic Tools (1985) (0)
Generating function zeros of Markov processes and their applications (2011) (0)
A stochastic four-color theorem (2014) (0)
The Law of Large Numbers and 4 (2016) (0)
Continuous time Markov chains (2010) (0)
One-dependent colorings of the star graph (2018) (0)
Linear Systems with Values in [0, ∞) s (2005) (0)
Random arithmetic-geometric means and random pi: observations and conjectures (1992) (0)
Probability Measures on Metric Spaces (1969) (0)
INHOMOGENEOUS AND RANDOM ENVIRONMENTS1 (2016) (0)
STATIONARY DISTRIBUTIONS AND CORRELATION INEQUALITIES FOR ASYMMETRIC EXCLUSION PROCESSES (2013) (0)
The Symmetric Exclusion Process: Correlation Inequalities and Applications T. Liggett. UCLA (2008) (0)
The Construction, and Other General Results (1985) (0)
One-dependent hard-core processes and colorings of the star graph (2018) (0)
PR ] 2 6 Ju n 20 09 A RECURSIVE PROOF OF ALDOUS ’ SPECTRAL GAP (0)

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