 97559 Remco van der Hofstad, Frank den Hollander, Gordon Slade.
 A new inductive approach to the lace expansion for selfavoiding walks
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Oct 27, 97

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Abstract. We introduce a new inductive approach to the lace expansion, and apply
it to prove Gaussian behaviour for the weakly selfavoiding walk on
${\Bbb Z}^d$ where loops of length $m$ are penalised by a factor
$e^{\beta/m^{p}}$ ($0<\beta \ll 1$) when:\\
(1) $d>4$, $p \geq 0$; \\
(2) $d \leq 4$, $p > \frac{4d}{2}$. \\
In particular, we derive results first obtained by Brydges and Spencer
(and revisited by other authors) for the case $d>4$, $p=0$. In addition,
we prove a local central limit theorem, with the exception of the
case $d>4$, $p=0$.
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