- 06-291 Roberto Fernandez and Aldo Procacci
- Cluster expansion for abstract polymer models.
New bounds from an old approach
Oct 18, 06
(auto. generated ps),
of related papers
Abstract. We revisit the classical approach to cluster expansions, based on
tree graphs, and establish a new convergence
condition that improves those by Koteck\'y-Preiss and
Dobrushin, as we show in some examples. The two ingredients
of our approach are: (i) a careful consideration of the Penrose identity
for truncated functions, and (ii) the use of iterated transformations
to bound tree-graph expansions.