  Depletion of natural and artificial resources is a fundamental problem and a
potential cause of economic crises, ecological catastrophes, and death of
living organisms. Understanding the depletion process is crucial for its
further control and optimized replenishment of resources. In this paper, we
investigate a stock depletion by a population of species that undergo an
ordinary diffusion and consume resources upon each encounter with the stock. We
derive the exact form of the probability density of the random depletion time,
at which the stock is exhausted. The dependence of this distribution on the
number of species, the initial amount of resources, and the geometric setting
is analyzed. Future perspectives and related open problems are discussed.

Statistical Mechanics;Biological Physics;Chemical Physics