Vladimir Palyulin
TU Munich

Search reliability and hitting times of Levy flights and Brownian motion

The feasibility and efficiency of reaching a certain point in a search space depends on a search strategy. Naturally, the strategy should optimise the efficiency of a search. We will discuss a different definitions of efficiency in the context of 1D space search. Then we will compare the performance of scale-free, Brownian and combined strategies. As a scale-free strategy the Levy flight motion will be considered. Contrary to the popular opinion that scale-free strategies optimise search for sparse targets, we will show that Brownian motion can outperform Levy flights, while combined strategy always outperforms Levy flights. Then we will show that the hitting probability depends on the strategy and can adopt values between 0 and 1 even in the absence of complex potential energy landscape.