32 citations · 32 across the 1 of their papers we have counts for
4 papers
The Brown-Colbourn conjecture on zeros of reliability polynomials is false
Gordon Royle, Alan D. Sokal
We give counterexamples to the Brown-Colbourn conjecture on reliability polynomials, in both its univariate and multivariate forms. The multivariate Brown-Colbourn conjecture is fa…
Homogeneous multivariate polynomials with the half-plane property
Young-Bin Choe, James G. Oxley, Alan D. Sokal +1
A polynomial P in n complex variables is said to have the "half-plane property" (or Hurwitz property) if it is nonvanishing whenever all the variables lie in the open right half-pl…
A Personal List of Unsolved Problems Concerning Lattice Gases and Antiferromagnetic Potts Models
Alan D. Sokal
I review recent results and unsolved problems concerning the hard-core lattice gas and the q-coloring model (antiferromagnetic Potts model at zero temperature). For each model, I c…
Monte Carlo Methods for the Self-Avoiding Walk
Alan D. Sokal
This article is a pedagogical review of Monte Carlo methods for the self-avoiding walk, with emphasis on the extraordinarily efficient algorithms developed over the past decade.