How anomalous becomes normal: Lévy walks in physics, biology, and our life

Mentioning of a random walk model typically comes together with an image of drunkard's walk as way of introducing a model or with a classical Brownian diffusion as an example of the corresponding physical process. In this talk, we will discuss models of random walks leading to stochastic transport processes which are markedly different from classical diffusion and thus often referred to as “anomalous”. In the so-called Lévy walk model, a random walking particle may undertake very long excursions with a diverging mean squared length, however, in doing so it always moves with a constant speed. This combination is the key feature of the model which made it so successful in describing a vast number of real-world dispersal phenomena in physics, biology and in our everyday life. I will describe the setup of the basic Lévy walk model and its generalisations, illustrate it by several applications and try to outline some open questions in the field.