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In this talk we will introduce and discuss a branching-selection process in which we have a fixed number, N, of branching Brownian motions, with deletion of particles at each branching event in order to keep the population sized fixed. The rate of deletion will be dependent on the rank of the particle. In particular we will discuss their hydrodynamic limits of the system as N goes to infinity, and a weak selection principle, including elements of the proof. We will also discuss how these models are connected to the ‘inverse first passage problem’, which is a problem arising in risk modelling.
