Orateur
Lena Kuwata
(MAP5, Université Paris Cité)
Description
We introduce a spatial branching process to model the growth of the mycelial network of a filamentous fungus. In this model, each filament is described by the position of its tip, the trajectory of which is the solution to a stochastic differential equation with a drift term which depends on all the other trajectories. Each filament can branch either at its tip or along its length, that is to say at some past position of its tip, at some time- and space-dependent rates. It can stop growing at some rate which also depends on the positions of the other tips. We study the large population limit of this process and we characterise the limiting process as the weak solution to a system of partial differential equations.
