FLUCTUATIONS IN A LEVY FLIGHT GAS

We consider the density fluctuations of an ideal Brownian gas of particles performing Levy flights characterized by the index f. We find that the fluctuations scale as DELTA-N(t) approximately t(H), where the Hurst exponent H locks onto the universal value 1/4 for Levy flights with a finite root-mean-square range (f > 2). For Levy flights with a finite mean range but infinite root-mean-square range (1 < f < 2) the Hurst exponent H = 1/(2f). For infinite-range Levy flights (f < 1) the Hurst exponent locks onto the value 1/2. The corresponding power spectrum scales with an exponent 1 + 2H, independent of dimension.