74 citations · 158 across the 17 of their papers we have counts for
20 papers
One-dependent colorings of the star graph
Thomas M. Liggett, Wenpin Tang
This paper is concerned with symmetric -dependent colorings of the -ray star graph for . We compute the critical point of the -dependent hard-core…
Multivariate CLT follows from strong Rayleigh property
Subhroshekhar Ghosh, Thomas M. Liggett, Robin Pemantle
Let be random variables taking nonnegative integer values and let be the probability generating function. Suppose that is real sta…
Symmetric 1-Dependent Colorings of the Integers
Alexander E. Holroyd, Thomas M. Liggett
In a recent paper by the same authors, we constructed a stationary 1-dependent 4-coloring of the integers that is invariant under permutations of the colors. This was the first sta…
Finitely dependent coloring
Alexander E. Holroyd, Thomas M. Liggett
We prove that proper coloring distinguishes between block-factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficient…
Scale-free and power law distributions via fixed points and convergence of (thinning and conditioning) transformations
Richard Arratia, Thomas M. Liggett, Malcolm J. Williamson
In discrete contexts such as the degree distribution for a graph, \emph{scale-free} has traditionally been \emph{defined} to be \emph{power-law}. We propose a reasonable interpreta…
T. E. Harris' contributions to interacting particle systems and percolation
Thomas M. Liggett
Interacting particle systems and percolation have been among the most active areas of probability theory over the past half century. Ted Harris played an important role in the earl…