Al-Khwarizmi
Applied Mathematics Webinar 

Next talk : June 9, 2026. 

Tuesday - 2:00 pm (GMT) 

Zoom link: https://ksu-hub.zoom.us/j/97753107489

Speaker: Grégory Schehr, Sorbonne university, Paris, France. 

Title: Universal distribution of the number of minima for constrained random walks and Lévy flights. 

Abstract: We compute exactly the full distribution of the number m of local minima in a one-dimensional landscape generated by a random walk or a Lévy flight. We consider two different ensembles of landscapes, one with a fixed number of steps N and the other till the first-passage time of the random walk to the origin. We show that  the distribution of m is drastically different in the two ensembles (Gaussian in the former case,  while having a power-law tail with exponent -3/2 in the latter case). However, the most striking aspect of our results is that, in each case, the distribution is completely universal for all m (and not just for large m), i.e., independent of the jump distribution in the random walk. This means that the distributions are exactly identical for Lévy flights and random walks with finite jump variance.