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arXiv · 1402.5389

On the spread of a branching Brownian motion whose offspring number has infinite variance

Jean Avan·Nicolas Grosjean·Thierry Huillet
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Abstract

We study the impact on shape parameters of an underlying Bienaym\'e-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then consider spatial branching processes in dimension d, not necessarily integer. The underlying branching mechanism is then either a binary branching model or one presenting infinite variance. In particular we evaluate the chance p(x) of being hit if the epidemics started away at distance x. We compute the large x tail probabilities of this event, both when the branching mechanism is regular and when it exhibits very large fluctuations.

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Jean Avan, Nicolas Grosjean, Thierry Huillet. 2014-02-21. On the spread of a branching Brownian motion whose offspring number has infinite variance. https://arxiv.org/abs/1402.5389

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