# Quantifying the threshold phenomena for propagation in nonlocal diffusion equations

@inproceedings{Alfaro2022QuantifyingTT, title={Quantifying the threshold phenomena for propagation in nonlocal diffusion equations}, author={Matthieu Alfaro and Arnaud Ducrot and Hao Kang}, year={2022} }

We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such phenomena. The outcomes dramatically depend on the tails of the dispersal kernel and can take a large variety of different forms. The strategy is to combine sharp estimates of the tails of the sum of i.i.d. random variables (coming, in particular, from large…

## One Citation

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

- Mathematics
- 2022

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…

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