  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.
