Depletion-controlled starvation of a diffusing forager.

Area of Science:

• Statistical Physics
• Stochastic Processes
• Random Walks

Background:

• Lattice random walks are fundamental models in statistical physics.
• Understanding walker behavior under resource constraints, like food, is crucial for various applications.

Purpose of the Study:

• To analyze the starvation dynamics of a lattice random walker with limited food consumption capacity.
• To determine how the spatial dimension influences the average lifetime and exploration patterns of the walker.

Main Methods:

• Mathematical modeling of a lattice random walker with a food-dependent step limit.
• Analytical calculations of the average lifetime (⟨τ⟩) in different spatial dimensions (d).

Main Results:

• In 1D, average lifetime ⟨τ⟩ is proportional to the step limit S.
• For d>2, ⟨τ⟩ exhibits exponential dependence on S (⟨τ⟩≃exp(S^{ω})), suggesting an infinite upper critical dimension.
• In 2D, ⟨τ⟩ scales as S^{z} with z≈2.

Conclusions:

• The spatial dimension significantly alters the starvation dynamics and lifetime of the random walker.
• Long-lived walks tend to stay near food sources, exploring complex, ramified regions.
• The distinct site visitation distribution deviates from single-parameter scaling.