Stochastization in gravitating systems

We discuss the effective stochastization time τ e for gravitating systems in terms of the Krylov and GurzadyanSavvidi paradigm. The truncated Holtsmark distribution for a random force proposed by Rastorguev and Sementsov implies τ e /τ c α N 0.20 , where τ c is the crossing time. We find in the case of the Petrovskaya distribution for a random force τ e /τ c α N k , where k = 0.27–0.31, depending on the oblateness and rotation of the system, and τ e /τ c α N 1/3 /(ln N) 1/2 when N » 1. The latter result agrees with those of Genkin (1969) and Gurzadyan & Kocharyan (2009) (k = 1/3). (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)