Proceedings 38th Annual Symposium on Foundationsâ€¦

19 October 1997

TLDR

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

The proof of correctness of the algorithm relies on recent theory of rapidly mixing Markov chains and isoperimetric inequalities to show that a certain random walk can be used to sample nearly uniformly from within K within Euclidean space.Expand

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

A related Markov chain for d-regular graphs on a varying number of vertices is introduced and it is proved that the related chain has mixing time which is bounded by a polynomial in N, the expected number of Vertices, under reasonable assumptions about the arrival and departure process.Expand

40th Annual Symposium on Foundations of Computerâ€¦

17 October 1999

TLDR

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

This work describes and investigates a third class of counting problems, of intermediate complexity, that is not known to be identical to (i) or (ii), and can be characterised as the hardest problems in a logically defined subclass of #P.Expand