Random walk models are excellent analytical tools for addressing a number of important questions of statistical physics: various transport processes including normal and anomalous diffusion, aging, memory effects, finite or random velocity of random walkers, and transport in active media. One of the most advanced models is the Lévy walk model, which we have recently reviewed (with Sergey Denisov, Augsburg University, and Josef Klafter, TAU). We continue to explore this model by extending its theory to higher dimensions and exploring its further applications.
Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations; I. Fouxon, S. Denisov, V. Zaburdaev, and E. Barkai, J. Phys. A: Math. Theor. 50, 154002 (2017)
Superdiffusive dispersals impart the geometry of underlying random walks; V. Zaburdaev, I. Fouxon, S. Denisov, and E. Barkai, Phys. Rev. Lett. 117, 270601 (2016)
Lévy walks; V. Zaburdaev, S. Denisov, J. Klafter, Rev. Mod. Phys. 87, 483 (2015)