How statistics of driven non-equilibrium systems appears from the theory of sample space reducing processes - all of it - from Gauss to Zipf

Sample space reducing (SSR) processes are simple path-dependent processes that offer an easy analytical understanding of the origin and ubiquity of power-laws in countless driven complex systems out of equilibrium. SSR processes exhibit generic power-laws - Zipf's law in particular. We show that SSR processes exhibit a much wider range of statistical diversity. Assuming that driving in a system is not uniformly strong within a system or across its life-span, but depends on the current state the system is in, we demonstrate that practically any distribution function can be naturally derived from SSR processes: Slow driving gives Zipf's law, constant driving leads to exact power-laws. More complicated driving processes yield exponential or Gamma distributions, normal distribution, Weibull, Gompertz, and Tsallis-Pareto distributions. We shortly discuss the areas of application of SRR processes that range from fragmentation processes, language formation, cascading processes,search processes, and multiplicative processes.

Friday, 15 March 2019, ore 11:30 — Aula Magna "Tullio Regge"