Samuel G. G. Johnston

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math.PR2026

Behaviour near explosion in continuous-time Galton-Watson trees

Simon C. Harris, Samuel G. G. Johnston, Juan Carlos Pardo

We study continuous-time Galton--Watson trees whose offspring generating function takes the form \begin{align} \label{eq:gen} f(s) = s - (1-s)^αL(1-s), \end{align} where $α\in (0,1…

math.PR2025

The Brownian marble

Samuel G. G. Johnston, Andreas Kyprianou, Tim Rogers +1

Let $R : (0, \infty) \to [0, \infty)$ be a measurable function. Consider coalescing Brownian motions started from every point in the subset ${(0, x) : x \in R}$ of $[0,\inf…