Condensation in critical Cauchy Bienaym\'e-Galton-Watson trees

21 Nov 2018 Kortchemski Igor Richier Loïc

We are interested in the structure of large Bienaym\'e-Galton-Watson random trees whose offspring distribution is critical and falls within the domain of attraction of a stable law of index $\alpha=1$. In stark contrast to the case $\alpha \in (1,2]$, we show that a condensation phenomenon occurs: in such trees, one vertex with macroscopic degree emerges... (read more)

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