  We consider the parabolic Anderson model $\partial u/\partial t =
\kappa\Delta u + \gamma\xi u$ with $u\colon\, \Z^d\times R^+\to \R^+$, where
$\kappa\in\R^+$ is the diffusion constant, $\Delta$ is the discrete Laplacian,
$\gamma\in\R^+$ is the coupling constant, and $\xi\colon\,\Z^d\times
\R^+\to\{0,1\}$ is the voter model starting from Bernoulli product measure
$\nu_{\rho}$ with density $\rho\in (0,1)$. The solution of this equation
describes the evolution of a "reactant" $u$ under the influence of a "catalyst"
$\xi$. In G\"artner, den Hollander and Maillard 2010 the behavior of the
\emph{annealed} Lyapunov exponents, i.e., the exponential growth rates of the
successive moments of $u$ w.r.t.\ $\xi$, was investigated. It was shown that
these exponents exhibit an interesting dependence on the dimension and on the
diffusion constant. In the present paper we address some questions left open in
G\"artner, den Hollander and Maillard 2010 by considering specifically when the
Lyapunov exponents are the a priori maximal value in terms of strong transience
of the Markov process underlying the voter model.

Probability