turkmath.org

In this talk, we present a model of random motion in a random environment, where a Brownian particle is moving among a dynamic field of Poissonian traps in $R^d$. We address some classical questions on this model, involving the survival probability and the optimal survival strategies of the Brownian particle from the trap field. We then discuss several variations of the model, including the discrete analogue in which Brownian motions are replaced by random walks and the continuum $R^d$ is replaced by the discrete lattice $Z^d$.