title: Depletion-controlled starvation of a diffusing forager.
abstract: We study the starvation of a lattice random walker in which each site initially contains one food unit and the walker can travel S steps without food before starving. When the walker encounters food, it is completely eaten, and the walker can again travel S steps without food before starving. When the walker hits an empty site, the time until the walker starves decreases by 1. In spatial dimension d=1, the average lifetime of the walker ⟨τ⟩∝S, while for d>2, ⟨τ⟩≃exp(S^{ω}), with ω→1 as d→∞; the latter behavior suggests that the upper critical dimension is infinite. In the marginal case of d=2, ⟨τ⟩∝S^{z}, with z≈2. Long-lived walks explore a highly ramified region so they always remain close to sources of food and the distribution of distinct sites visited does not obey single-parameter scaling.
authors.affiliation: Laboratorie de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France.
authors.forename: O
authors.initials: O
authors.lastname: Bénichou
authors.affiliation: Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: S
authors.initials: S
authors.lastname: Redner
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D017753:Ecosystem; D005502:Food; D008954:Models, Biological; D013217:Starvation; D016138:Walking