Large deviations and the emergence of a logarithmic delay in a nonlocal linearised Fisher-KPP equation

TL;DR

This paper investigates a nonlocal Fisher-KPP equation, demonstrating that large deviations lead to a logarithmic delay in wave propagation, extending previous results to a broader class of kernels.

Contribution

It establishes the emergence of a logarithmic delay in nonlocal Fisher-KPP equations using large deviations, applicable to all continuous symmetric thin-tailed kernels.

Findings

Logarithmic delay appears in solutions of the nonlocal Fisher-KPP equation.

The delay is shown to occur for a wide class of kernels, not just specific decay types.

Results extend previous work by relaxing decay assumptions on the kernel.

Abstract

We study a variant of the Fisher-KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a "Bramson-like" logarithmic delay for the linearised equation with step-like initial data. We conclude that the logarithmic delay emerges also for the solutions of the nonlinear equation. Previous papers found very precise results for the nonlinear equation with strong assumptions on the decay of the kernel. Our results are less precise, but they are valid for all continuous symmetric thin-tailed kernels.