Gerónimo Uribe Bravo, Universidad Nacional Autónoma de México
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In this talk, we will discuss a scaling limit for the sequence
of generation sizes of a (rooted plane) tree with a given degree sequence.
The main tools used in the proof include fluctuation theory and the
stability analysis of a time-change equation for exchangeable increment processes.
The scaling limit result extends and (probabilistically) proves a
conjecture by Aldous concerning the profile of conditioned
Galton-Watson trees first settled by Drmota and Gittenberger using
analytic combinatorics.