ATTRACTION TIME FOR STRONGLY REINFORCED WALKS
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Codina Cotar and Vlada Limic 
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We consider a class of strongly edge reinforced random walks,
where the corresponding reinforcement weight function is non-decreasing.
It is known by Limic and Tarr\`es (2007)
that the attracting edge emerges with probability 1, whenever the
underlying graph is locally bounded.
We study the asymptotic behavior of the tail distribution 
of the (random) time of attraction.
In particular, we obtain exact (up to multiplicative constant)
asymptotics if the underlying graph has two edges.
Next we show some extensions in the setting of finite and
bounded degree infinite graphs.
As a corollary we obtain that if the reinforcement weight has the form
$w(k) = k^\rho$, $\rho>1$, then (universally over finite graphs)
the expected time to attraction is infinite
if and only if $\rho \leq 1+ \frac{1+\sqrt{5}}{2}$.