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Lévy flights versus Lévy walks in bounded domains
Bartłomiej Dybiec1, Ewa Gudowska-Nowak1, Eli Barkai2
1Marian Smoluchowski Institute of Physics, and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland.
Physical Review. E
|June 17, 2017
Summary
Lévy walks and Lévy flights exhibit distinct behaviors on bounded domains. Their statistical similarities depend on boundary conditions and jump length distribution, impacting random walk analysis.
Area of Science:
- Physics
- Mathematics
- Statistical Mechanics
Background:
- Lévy flights and Lévy walks are fundamental random walk models with key differences in trajectory continuity and propagation velocity.
- Lévy flights possess pathological physical properties, often addressed by the Lévy walk concept.
Purpose of the Study:
- To explore and compare Lévy flight and Lévy walk models within bounded domains.
- To investigate the conditions under which these two models yield similar statistical outcomes.
Main Methods:
- Analytical investigation of random walk models.
- Numerical simulations to analyze model behaviors.
- Examination of statistical observables like survival probability and mean first passage time.
Main Results:
- The similarity between Lévy flights and Lévy walks is influenced by boundary conditions.
- The stability index of the jump length distribution significantly affects model convergence.
- Specific statistical observables show varying degrees of agreement between the two models.
Conclusions:
- Lévy flights and Lévy walks are not universally interchangeable, even in bounded systems.
- Understanding the interplay of boundary conditions and jump dynamics is crucial for accurate random walk modeling.
- The choice between Lévy flight and Lévy walk models depends on the specific physical system and desired observables.
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