The lace expansion on a tree with application to networks of self-avoiding walks
The paper provides new developments on the so-called lace expansion on a tree [introduced by \textit{D. Brydges} and \textit{T. Spencer}, Commun. Math. Phys. 97, 125-148 (1985; Zbl 0575.60099)] and applies the results so obtained to the analysis of cycle-free networks of mutually-avoiding spread-out self-avoiding walk on \(Z^d\) with \(d\) greater than four. The lace theory is generalized to deal with time variable indexed by a tree and the laces are classified in acyclic, cyclic and reductible laces. It is shown that for cycle-free network in dimension larger than four, the behaviour is Gaussian with sufficiently spread-out models.
scientific article; zbMATH DE number 1981407