Table of Contents

The question

When a population spreads into new territory — think a colony of bacteria growing outward on a plate — the shape of its advancing front isn’t smooth. It roughens, and the way it roughens turns out to carry a surprising amount of universal structure.

What we do

We use stochastic surface-growth models to explain the superdiffusive scaling seen in bacterial range-expansion experiments, connecting the coarse-grained front dynamics to KPZ universality and the non-Gaussian Tracy–Widom fluctuation statistics that come with it.

$$h(x, t) \sim v t + (\Gamma t)^{1/3}\, \chi$$

where $\chi$ follows a Tracy–Widom distribution — the fingerprint of the KPZ class.

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