Roberto Fernandez and Aldo Procacci
Cluster expansion for abstract polymer models. 
New bounds from an old approach
(64K, Latex)

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.