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Updated: Jul 26, 2025

Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion
Published on: January 15, 2016
Range-Controlled Random Walks
L Régnier1, O Bénichou1, P L Krapivsky2,3
1Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne Université, 75005 Paris, France.
Range-controlled random walks exhibit dimension-dependent critical exponents. Above this critical value, a forager can cover an infinite lattice in finite time, with surprising behaviors in multi-walker scenarios.
Area of Science:
- Physics
- Statistical Mechanics
- Mathematical Biology
Background:
- Random walks are fundamental models in physics and biology.
- Understanding how walkers explore spaces is crucial for various applications.
Purpose of the Study:
- To introduce and analyze range-controlled random walks.
- To determine the large-time behavior and distribution of the explored range.
- To investigate the impact of spatial dimension and competition on exploration.
Main Methods:
- Analysis of a one-parameter class of random walks with hopping rate N^a.
- Determination of average range and its distribution in limit cases.
- Study of two competing foragers with range-dependent hopping rates.
Main Results:
- A critical exponent a_d, dependent on spatial dimension d, governs exploration.
- For a > a_d, the forager covers the infinite lattice in finite time (a_1=2, a_d=1 for d>=2).
- In 1D, a single walker dominates for a>1, while walkers explore evenly for a<1.
Conclusions:
- The exponent 'a' and spatial dimension 'd' critically influence random walk exploration.
- Range-controlled walks offer tunable exploration dynamics.
- Competition between walkers leads to complex, dimension-dependent behaviors.
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