Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers.

We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda(c) and annihilation at rate lambda(a) . The test particle is annihilated at rate lambda(') on coming into contact with the other particles. The survival probability decays algebraically with time as t(-theta;) . The exponent theta; in d<2 is calculated using the perturbative renormalization group formalism as an expansion in epsilon=2-d . It is shown to be universal, independent of lambda(') , and to depend only on delta , the ratio of the diffusion constant of test particles to that of the other particles, and on the ratio lambda(a) / lambda(c) . In two dimensions we calculate the logarithmic corrections to the power law decay of the survival probability. Surprisingly, the logarithmic corrections are nonuniversal. The one-loop answer for theta; in one dimension obtained by setting epsilon=1 is compared with existing exact solutions for special values of delta and lambda(a) / lambda(c) . The analytical results for the logarithmic corrections are verified by Monte Carlo simulations.