Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A limit theorem for the contour process of conditioned Galton-Watson
  trees   In this work, we study asymptotics of the genealogy of Galton--Watson
processes conditioned on the total progeny. We consider a fixed, aperiodic and
critical offspring distribution such that the rescaled Galton--Watson processes
converges to a continuous-state branching process (CSBP) with a stable
branching mechanism of index $\alpha \in (1, 2]$. We code the genealogy by two
different processes: the contour process and the height process that Le Gall
and Le Jan recently introduced \cite{LGLJ1, LGLJ1}. We show that the rescaled
height process of the corresponding Galton--Watson family tree, with one
ancestor and conditioned on the total progeny, converges in a functional sense,
to a new process: the normalized excursion of the continuous height process
associated with the $\alpha $-stable CSBP. We deduce from this convergence an
analogous limit theorem for the contour process. In the Brownian case $\alpha
=2$, the limiting process is the normalized Brownian excursion that codes the
continuum random tree: the result is due to Aldous who used a different method.

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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg