 93195 Toth Balint
 The BondTrue SelfAvoiding Walk on Z.
II: Local Limit Theorem
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Jun 29, 93

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Abstract. The bondtrue selfavoiding walk is a nearest neighbour random
walk $X_n$ on $\Bbb Z$, for which the probability of jumping
along a bond of the lattice is proportional to
$\exp(g\cdot\text{number of previous jumps along that bond})$.
This paper is a continuation of T\'oth (1993), where the local
time process and first hitting times of $X_{\cdot}$ were
investigated. For formal definitions and notation see that
paper. Here we prove a local limit theorem, as
$\alpha\to\infty$, for the distribution of
$\alpha^{2/3}X_{\theta_{s/\alpha}}$, where $\theta_{s/\alpha}$
is a random time of geometric distribution with mean
$\left(1\text{e}^{s/\alpha}\right)^{1}=\frac\alpha s+O(1)$.
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