| 要約: | We provide a new characterisation of Duquesne and Le Gall's $\alpha$-stable
tree, $\alpha\in(1,2]$, as the solution of a recursive distribution equation
(RDE) of the form $\mathcal{T}\overset{d}{=}g(\xi,\mathcal{T}_i, i\geq0)$,
where $g$ is a concatenation operator, $\xi = (\xi_i, i\geq 0)$ a sequence of
scaling factors, $\mathcal{T}_i$, $i \geq 0$, and $\mathcal{T}$ are i.i.d.
trees independent of $\xi$. This generalises a version of the well-known
characterisation of the Brownian Continuum Random Tree due to Aldous, Albenque
and Goldschmidt. By relating to previous results on a rather different class of
RDE, we explore the present RDE and obtain for a large class of similar RDEs
that the fixpoint is unique (up to multiplication by a constant) and
attractive.
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