L\'evy walks

By Vasily Zaburdaev, S. Denisov, Joseph Klafter. 2014

457 citations recorded by the source corpus.

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The L\'{e}vy walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, bio-physics, and behavioral science demonstrate that this particular type of random walks provides significant insight into complex transport phenomena. This review provides a self-consistent introduction to L\'{e}vy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

Subfields: Applied Mathematics, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/4e6b5610923bfbb99bef68e763d5b3cdd9bc4589

Citations in the corpus

• Description of an ecological niche for a mixed local/nonlocal dispersal: An evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes (2021, unknown): “The importance of methods from probability and statistics to address the question of animal foraging also emerged in the analysis of the best strategy for the search of randomly located targets, see [28, 54, 56, 59].”