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The front location in branching Brownian motion with decay of mass

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We add a competitive interaction between nearby particles in a branching Brownian motion (BBM). Each particle has a mass, which decays at rate proportional to the local mass density at its location. The total mass increases through branching events. In standard BBM , we may define the front location at time t as the greatest distance of a particle from the origin. For the model with masses, it makes sense to instead define the front displacement as the distance at which the local mass density drops from Θ(1) to o(1). We can show that in a weak sense this front is ~ c t^{1/3} behind the front for standard BBM . I will discuss the proof of this result and progress on further results related to this model. This is joint work with Louigi Addario-Berry.

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