Ewan Davies
We demonstrate a quasipolynomial-time deterministic approximation algorithm for the partition function of a Gibbs point process interacting via a repulsive potential. This result holds for all activities $\lambda$ for which the partition function satisfies a zero-free assumption in a neighborhood of the interval $[0,\lambda]$. As a corollary, we obtain a quasipolynomial-time deterministic approximation algorithm for all $\lambda < e/\Delta_\phi$, where $\Delta_\phi$ is the potential-weighted connective cons
By implementing algorithmic versions of Sapozhenko's graph container methods, we give new algorithms for approximating the number of independent sets in bipartite graphs. Our first algorithm applies to $d$-regular, bipartite graphs satisfying a weak expansion condition: when $d$ is constant, and the graph is a bipartite $\Omega( \log^2 d/d)$-expander, we obtain an FPTAS for the number of independent sets. Previously such a result for $d> 5$ was known only for graphs satisfying the much stronger expansion co
For Δ≥5 and q large as a function of Δ, we give a detailed picture of the phase transition of the random cluster model on random Δ-regular graphs. In particular, we determine the limiting distribution of the weights of the ordered and disordered phases at criticality and prove exponential decay of correlations away from criticality. Our techniques are based on using polymer models and the cluster expansion to control deviations from the ordered and disordered ground states. These techniques also yield effic
Ewan Davies