Abstract Chechkin: From first passage and arrival for alpha-stable random motion to efficiency and reliability for Levy flight random search

Alpha-stable Levy motion stands for a class of non-Gaussian Markovian random processes whose stationary increments are distributed according to the Levy stable probability laws. Such process serves as a limit continuous-time description of Levy flight (LF), a discrete-time random walk whose jumps or flights exhibit a scale-free heavy-tailed distribution with infinite variance. It is generally believed that Levy flights optimize random search for sparse targets. In the present talk we give a short review of temporal and spatial properties of alpha-stable motion, focusing on the distinction between the first passage (or first escape) and first arrival phenomena. Based on this probabilistic background, we study the efficiency of several minimalist search models based on pure and combined Levy flight search strategies, in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space). We deduce certain common patterns from these models.

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