## Incest and infanticide: a branching process with deletions and mergers that matches the threshold for hypercube percolation

Series
Combinatorics Seminar
Time
Friday, April 8, 2022 - 3:00pm for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Fiona Skerman – Uppsala University / Simon&#039;s Institute – fiona.skerman@math.uu.sehttps://fskerman.github.io/
Organizer

We define a graph process based on a discrete branching process with deletions and mergers, which is inspired by the 4-cycle structure of the hypercube $\mathcal{Q}_d$ for large $d$. We prove survival and extinction under certain conditions on $p$ and $q$ that heuristically match the known expansions of the critical probabilities for bond percolation on the hypercube. Joint work with Laura Eslava and Sarah Penington. Based on https://arxiv.org/abs/2104.04407.