Exponentially Tempered Lévy Sums in Random Lasers

Lévy fluctuations have associated infinities due to diverging moments, a problem that is circumvented by putting restrictions on the magnitude of the fluctuations, realizing a process called the truncated Lévy flight. We show that a perfect manifestation of this exotic process occurs in coherent random lasers, and it turns out to be the single underlying explanation for the complete statistical behavior of nonresonant random lasers. A rigorous parameter estimation of the number of summand variables, the truncation parameter, and the power-law exponent is carried out over a wide range of randomness, inversion, and system size. Random laser intensity is modeled on a unique platform of exponentially tempered Lévy sums. The computed behavior exhibits an excellent agreement with the experimentally observed fluctuation behavior.