= Earliest diffusive target encounter among independent searchers
{title2=$\tau\simeq V/(Nk_a)$}
If $N$ independent well-mixed searchers each encounter a small absorbing target with approximate exponential hazard $k_a/V$, their minimum waiting time has hazard $Nk_a/V$. The <Smoluchowski association rate> is $k_a=4\pi D_{\rm rel}r_0$. Cell geometry, orientational capture and nonequilibrium spatial distributions can change this idealized estimate; an arbitrary nonexponential first-passage mean does not in general divide by $N$ exactly.
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