Depletion-Controlled Starvation of a Diffusing Forager
Laboratoire de Physique Théorique de la Matière Condensée, France
What is the fate of a random-walk forager that depletes its environment as it wanders? Whenever the forager lands on a food-containing site, all the food is consumed and the forager becomes fully sated. However, when the forager lands on an empty site, it moves one time unit to starvation. If the forager wanders S steps without encountering food, it starves to death. We show that the lifetime of this starving random walk forager scales linearly with S in one dimension by solving an underlying non-Markovian first-passage problem. In greater that two dimensions, we present evidence that the lifetime grows quasi-exponentially in S.