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We consider a diffusing particle, with diffusion constant D', moving in onedimension in an infinite sea of noninteracting mobile traps with diffusionconstant D and density rho. We show that the asymptotic behavior of thesurvival probability, P(t), is given by P(t) ~ exp[-4 rho(Dt/pi)^{1/2}],independent of D'. The result comes from obtaining upper and lower bounds onP(t), and showing that they coincide asymptotically. We also obtain exactresults for P(t) to first order in D' for an arbitrary finite number of traps.Comment: Minor revisions; new results for d>

Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps