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 sho...

Let H~ be the height of a random binary search tree on n nodes. We show that there exists constants a = 4.31107.. . and/3 = 1.95.. . such that E(H~) = c~logn / 3 1 o g l o g n + O(1), We also show that Var(H~) = O(1).

Formal analysis of software is a powerful analysis tool, but can be too costly. Random search of formal models can reduce that cost, but is theoretically incomplete. However, random search of finite-state machines exhibits an early saturation effect, i.e., random search quickly yields all that can be found, even after a much longer search. Hence, we avoid the theoretical problem of incompletene...

A class of nonparametric regression function estimates generalizing the nearest neighbor estimate of Cover [ 121 is presented. Under various noise conditions, it is shown that the estimates are strongly uniformly consistent. The uniform convergence of the estimates can be exploited to design a simple random search algorithm for the global minimization of the regression function.