A new approach to the coupling technique, which is called path coupling, for bounding mixing rates, is illustrated, which may allow coupling proofs which were previously unknown, or provide significantly better bounds than those obtained using the standard method.Expand

A hierarchy of relaxations obtained by combining enumeration of initial sequences with Smith's rule can be formulated as a linear programming problem in an enlarged space of variables and new valid inequalities for the problem are obtained.Expand

The theorems provide the first proof of #P-completeness of the partition function of certain models from statistical physics, such as the Widom–Rowlinson model, even in graphs of maximum degree 3.Expand

It is shown that the variance of the number of solutions can be used to set bounds on the phase transition and to indicate the accuracy of the prediction.Expand

Algorithms for linear programming problems with two or three variables and n constraints are described, improving the previously known best bounds of $O(n\log n)$ time.Expand

We present a randomised polynomial time algorithm for approximating the volume of a convex body K in n -dimensional Euclidean space. The proof of correctness of the algorithm relies on recent theory… Expand

Two results are proved concerning approximate counting of independent sets in graphs with constant maximum degree $\Delta$ that imply that the Markov chain Monte Carlo technique is likely to fail and that no fully polynomial randomized approximation scheme can exist for $\Delta \geq 25$ unless $\mathrm{RP}=\mathrm(NP)$.Expand

A new Markov chain is defined on k-colourings of graphs, and its convergence properties are related to the maximum degree ∆ of the graph, and it is shown to have bounds on convergence time appreciably better than those for the wellknown Jerrum/Salas–Sokal chain in most circumstances.Expand

We show that computing the volume of a polyhedron given either as a list of facets or as a list of vertices is as hard as computing the permanent of a matrix.