Role of depletion on the dynamics of a diffusing forager

@article{Benichou2016RoleOD,
  title={Role of depletion on the dynamics of a diffusing forager},
  author={Olivier B'enichou and Marie Chupeau and Sidney Redner},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2016},
  volume={49}
}
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… 

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