Depletion of Resources by a Population of Diffusing Species

Abstract

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.

References in corpus (43)

• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Stochastic Resetting and Applications
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Extreme value statistics of correlated random variables: a pedagogical review
• Diffusion-limited reactions in dynamic heterogeneous media
• Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
• Paradigm shift in diffusion-mediated surface phenomena
• The Local and the Occupation Time of a Particle Diffusing in a Random Medium
• Mortality, Redundancy, and Diversity in Stochastic Search
• Diffusive escape through a narrow opening: new insights into a classic problem
• Occupation Time Statistics in the Quenched Trap Model
• Universal Formula for Extreme First Passage Statistics of Diffusion
• Distribution of extreme first passage times of diffusion
• The escape problem for mortal walkers
• From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of $N$ random walkers
• First passage statistics for diffusing diffusivity
• Explicit Construction of the Brownian Self-Transport Operator
• Residence Time Distribution for a Class of Gaussian Markov Processes
• First passage time statistics for two-channel diffusion
• Asymptotics of extreme statistics of escape time in 1,2 and 3-dimensional diffusions
• Depletion-Controlled Starvation of a Diffusing Forager
• A probabilistic approach to extreme statistics of Brownian escape times in dimensions 1, 2, and 3
• Competition between slow and fast regimes for extreme first passage times of diffusion
• Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains
• Theory of diffusion-influenced reactions in complex geometries
• Semi-analytical computation of Laplacian Green functions in three-dimensional domains with disconnected spherical boundaries
• A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models
• Surface Hopping Propagator: An Alternative Approach to Diffusion-Influenced Reactions
• Explore or exploit? A generic model and an exactly solvable case
• Survival probability of stochastic processes beyond persistence exponents
• Statistics of boundary encounters by a particle diffusing outside a compact planar domain
• Role of Depletion on the Dynamics of a Diffusing Forager
• Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets
• Universality classes of foraging with resource renewal
• Residence time statistics for $N$ blinking quantum dots and other stochastic processes
• First exit times and residence times for discrete random walks on finite lattices
• Optimally Frugal Foraging
• On the joint residence time of N independent two-dimensional Brownian motions
• Statistics of the occupation time of renewal processes
• Order statistics of the trapping problem
• Does Greed Help a Forager Survive?
• Random Search with Memory in Patchy Media: Exploration-Exploitation Tradeoff

Cited by in corpus (10)

• Search efficiency in the Adam-Delbrück reduction-of-dimensionality scenario versus direct diffusive search
• Statistics of diffusive encounters with a small target: Three complementary approaches
• Extreme hitting probabilities for diffusion
• First-passage times of multiple diffusing particles with reversible target-binding kinetics
• Encounter-based approach to diffusion with resetting
• An encounter-based approach to the escape problem
• Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
• Escape-from-a-layer approach for simulating the boundary local time in Euclidean domains
• The Steklov problem for exterior domains: asymptotic behavior and applications
• Encounter-based approach to target search problems: a review