Emmanuel Schertzer

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math.PR2025

Stochastic neutral fractions and the effective population size

RaphaÃ«l Forien, Emmanuel Schertzer, ZsÃ³fia TalyigÃ¡s +1

The dynamics of a general structured population is modelled using a general stochastic differential equation (SDE) with an infinite decomposability property. This property allows t…

math.PR2025

$K$ -Branching Random Walk with Noisy Selection: Large Population Limits and Phase Transitions

Colin Desmarais, Emmanuel Schertzer, ZsÃ³fia TalyigÃ¡s

We analyze a variant of the Noisy $K$ -Branching Random Walk, a population model that evolves according to the following procedure. At each time step, each individual produces a lar…

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…

Stochastic neutral fractions and the effective population size

K-Branching Random Walk with Noisy Selection: Large Population Limits and Phase Transitions

The Brownian marble

$K$ -Branching Random Walk with Noisy Selection: Large Population Limits and Phase Transitions