Jiayan Guo

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math.PR2025

The Genealogy of Conditioned Critical Galton--Watson Trees

Jiayan Guo, Wenming Hong

Let $T$ be the random family tree associated with the critical Galton--Watson process ${Z_{n}}_{n \geq 0}$ . Geiger (1999) provided an explicit representation of the law of $T$ cond…

math.PR2025

Precise Large Deviations for the Total Population of Heavy-tailed Critical Branching Processes with Immigration

Jiayan Guo, Wenming Hong

We focus on the partial sum $S_{n} = X_{1} + \dots + X_{n}$ of the critical branching process with immigration ${X_{n}}$ , when the offspring $I^¾$ is regularly varying with index $Î½+1…