# Sesqui-type branching processes

## TL;DR

This paper analyzes a special two-type branching process where only one type reproduces, providing key estimates for survival and total particles, which are crucial for understanding certain random graph processes.

## Contribution

It introduces and analyzes a two-type branching process with a barren type, offering new estimates for survival probability and total particles, relevant for bounded-size Achlioptas processes.

## Key findings

- Derived survival probability estimates
- Established tail bounds for total particles
- Linked results to bounded-size Achlioptas processes

## Abstract

We consider branching processes consisting of particles (individuals) of two types (type L and type S) in which only particles of type L have offspring, proving estimates for the survival probability and the (tail of) the distribution of the total number of particles. Such processes are in some sense closer to single- than to multi-type branching processes. Nonetheless, the second, barren, type complicates the analysis significantly. The results proved here (about point and survival probabilities) are a key ingredient in the analysis of bounded-size Achlioptas processes in a recent paper by the last two authors.