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The problem of a diffusing particle moving among diffusing traps is analyzedin general space dimension d. We consider the case where the traps areinitially randomly distributed in space, with uniform density rho, and deriveupper and lower bounds for the probability Q(t) (averaged over all particle andtrap trajectories) that the particle survives up to time t. We show that, for1<=d<2, the bounds converge asymptotically to give $Q(t) \sim exp(-\lambda_dt^{d/2})$ where $\lambda_d = (2/\pi d) sin(\pi d/2) (4\pi D)^{d/2} \rho$ and Dis the diffusion constant of the traps, and that $Q(t) \sim exp(- 4\pi\rho Dt/ln t)$ for d=2. For d>2 bounds can still be derived, but they no longerconverge for large t. For 1<=d<=2, these asymptotic form are independent of thediffusion constant of the particle. The results are compared with simulationresults obtained using a new algorithm [V. Mehra and P. Grassberger, Phys. Rev.E v65 050101 (2002)] which is described in detail. Deviations from thepredicted asymptotic forms are found to be large even for very small values ofQ(t), indicating slowly decaying corrections whose form is consistent with thebounds. We also present results in d=1 for the case where the trap densities oneither side of the particle are different. For this case we can still obtainexact bounds but they no longer converge.Comment: 13 pages, RevTeX4, 6 figures. Figures and references updated;  equations corrected; discussion clarifie

Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps