  We consider the probability $P(t)$ that a given site remains unvisited by any
of a set of random walkers in $d$ dimensions undergoing the reaction $A+A\to0$
when they meet. We find that asymptotically $P(t)\sim t^{-\theta}$ with a
universal exponent $\theta=\ffrac12-O(\epsilon)$ for $d=2-\epsilon$, while, for
$d>2$, $\theta$ is non-universal and depends on the reaction rate. The
analysis, which uses field-theoretic renormalisation group methods, is also
applied to the reaction $kA\to0$ with $k>2$. In this case, a stretched
exponential behaviour is found for all $d\geq1$, except in the case $k=3$,
$d=1$, where $P(t)\sim {\rm e}^{-\const (\ln t)^{3/2}}$.
