Survival probability of a mobile particle in a fluctuating field

We study the survival probability $P(t)$, up to time t, of a test particle moving in a fluctuating external field. The particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field that it ``sees'' at its own location does not change sign. This is a natural generalization of the ``static persistence'' (when the particle is at rest), which has generated considerable interest recently. Two types of particle motion are considered. In one case the particle adopts a strategy to live longer and in the other it just diffuses randomly. Three different external fields were considered: (i) the solution of diffusion equation, (ii) the ``color'' profile of the q-state Potts model undergoing zero-temperature coarsening dynamics, and (iii) spatially uncorrelated Brownian signals. In most cases studied, P(t)~t^-θₘ for large t. The exponent θₘ is calculated numerically, analytically by approximate methods, and in some cases exactly. It is shown in some special cases that the survival probability of the mobile particle is related to the persistence of special ``patterns'' present in the initial configuration of a phase-ordering system.