Asymmetric Lévy Flights Are More Efficient in Random Search

We study the first-arrival (first-hitting) dynamics and efficiency of a one-dimensional random search model performing asymmetric Lévy flights by leveraging Fokker–Planck equation with δ-sink an space-fractional derivative operator stable index α asymmetry (skewness) parameter β. find exact analytical results for probability density times efficiency, we analyse their behaviour within limits short long times. that when starting point searcher is to right target, Brownian motion more efficient than β≤0 (with rightward bias) initial distances, while β>0 leftward α→1 are efficient. When increasing distance flight (except α=1 β=0) search. Moreover, in jumps leads essentially higher compared symmetric at both effect pronounced indices close unity.