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Reinforced Galton-Watson processes.

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SSDW01 - Self-interacting processes

In a reinforced Galton-Watson process with  reproduction law $\nu$ and memory parameter $q\in(0,1)$, the number of children of a typical individual either, with probability$q$, repeats that of one of its forebears picked uniformly at random, or, with complementary probability  $1-q$, is given by an independent sample from $\nu$. We estimate the average size of the population at a large generation, and in particular, we determine explicitly the  Malthusian growth rate in terms of $\nu$ and $q$. Our approach via the analysis of transport equations  owes much to works by Flajolet and co-authors. This talk is based on joint works with Bastien Mallein (Toulouse)

This talk is part of the Isaac Newton Institute Seminar Series series.

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