  We study the dynamics of a starving random walk in general spatial dimension
$d$. This model represents an idealized description for the fate of an unaware
forager whose motion is not affected by the presence or absence of resources.
The forager depletes its environment by consuming resources and dies if it
wanders too long without finding food. In the exactly-solvable case of one
dimension, we explicitly derive the average lifetime of the walk and the
distribution for the number of distinct sites visited by the walk at the
instant of starvation. We also give a heuristic derivation for the averages of
these two quantities. We tackle the complex but ecologically-relevant case of
two dimensions by an approximation in which the depleted zone is assumed to
always be circular and which grows incrementally each time the walk reaches the
edge of this zone. Within this framework, we derive a lower bound for the
scaling of the average lifetime and number of distinct sites visited at
starvation. We also determine the asymptotic distribution of the number of
distinct sites visited at starvation. Finally, we solve the case of high
spatial dimensions within a mean-field approach.
