T. Liggett

most citedHow likely is an i.i.d. degree sequence to be graphical?

12 citations · 19 across the 3 of their papers we have counts for

collaborators

3 papers

math.PR2005★ 7 cited

Conditional Association and Spin Systems

Thomas M. Liggett

A 1977 theorem of T. Harris states that an attractive spin system preserves the class of associated probability measures. We study analogues of this result for measures that satisf…

math.PR2005★ 12 cited

How likely is an i.i.d. degree sequence to be graphical?

Richard Arratia, Thomas M. Liggett

Given i.i.d. positive integer valued random variables D_1,...,D_n, one can ask whether there is a simple graph on n vertices so that the degrees of the vertices are D_1,...,D_n. We…

math.PR2003

Integrals, Partitions, and Cellular Automata

Alexander E. Holroyd, Thomas M. Liggett, Dan Romik

We prove that $\int_{0}^{1} \frac{- lo g f ( x )}{x} d x = \frac{π ^{2}}{3 ab}$ where $f (x)$ is the decreasing function that satisfies $f^{a} - f^{b} = x^{a} - x^{b}$ , for $0 < a < b$ . When $a$ is an integer and $b=…