Strong clumping of super-Brownian motion in a stable catalytic medium
The authors study the evolution of the mass of clusters at spatially rare sites developped by the long time behaviour of the continuous super-Brownian motion in a stable catalytic medium. The mass of each cluster evolves independently according to a non-Markovian continuous process trapped at mass zero, which is described by means of a Brwonian snake construction in random medium. The authors give a functional limit theorem which describes the phenomenon: As a limit one obtains a Poisson point field of mass clusters with no spatial motion component and with infinite variance. Survival probabilities and asymptotic sizes are also studied.
annealed and quenched random medium approaches
scientific article; zbMATH DE number 1906108