Abstract:

We consider independent random walks with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates, we obtain a strong law of large numbers for the density of particles in the supremum norm, which limit is given by a semilinear heat equation with source of type x^p, p between 1 and 3. It is also proved that the explosion time converges in probability to the explosion time of the PDE.

Joint work with P. Groisman (Universidad de Buenos Aires).