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Updated: Jul 26, 2025

Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion

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Published on: January 15, 2016

Range-Controlled Random Walks.

L Régnier¹, O Bénichou¹, P L Krapivsky^2,3

¹Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne Université, 75005 Paris, France.

Physical Review Letters

|June 16, 2023

Summary

This summary is machine-generated.

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.

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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.