P(L)\propto L^{-m}.

Here, the exponents m range from 1 to 3 and the resulting stationary PDF of visited sites P(x,y) is not Gaussian.In a 1999 Nature paper, G.M. Viswanathan shows that such powerlaw foraging (with exponent m=2) can be an optimum search strategy if target sites are sparse and can be visited repeatedly.

For an intuitive understanding, he notes:

- In a Levi flight, irrespective of the exponent, the probability of returning to a previously visited site is smaller than for a Brownian walk with Gaussian PDF.

- Also, N Levy walkers visit much more new sites than N Brownian walkers.

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