Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-02-17
Phys. Rev. E vol. 83, pp. 061125, (2011)
Physics
Condensed Matter
Statistical Mechanics
4 pages; 4 figures
Scientific paper
10.1103/PhysRevE.83.061125
We study the one-dimensional Levy stable density distributions g(alpha, beta; x) for -infty < x < infty, for rational values of index alpha and the asymmetry parameter beta: alpha = l/k and beta = (l - 2r)/k, where l, k and r are positive integers such that 0 < l/k < 1 for 0 <= r <= l and 1 < l/k <= 2 for l-k <= r <= k. We treat both symmetric (beta = 0) and asymmetric (beta neq 0) cases. We furnish exact and explicit forms of g(alpha, beta; x) in terms of known functions for any admissible values of alpha and beta specified by a triple of integers k, l and r. We reproduce all the previously known exact results and we study analytically and graphically many new examples. We point out instances of experimental and statistical data that could be described by our solutions.
Gorska Katarzyna
Penson Karol A.
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