On the Origin of Fat Tailed Distribution Functions in Driven Complex Systems

Explore the origins of fat-tailed distribution functions in driven complex systems through this 45-minute conference talk by Stefan Thurner at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the concept of sample space reducing (SSR) processes, which offer an intuitive understanding of the prevalence of fat-tailed distributions, including power-laws, in numerous complex systems. Learn how SSR processes provide a mathematically simple and exact alternative to Boltzmann equation-based approaches for non-equilibrium systems. Discover how the statistics of driven systems are often determined by the driving process and exhibit universality regardless of specific relaxation dynamics. Examine how simple driving processes can naturally derive various distributions, including Zipf's law, power-laws, exponential, Gamma, normal, Weibull, Gompertz, and Pareto distributions. Explore practical examples of SSR processes in fragmentation processes, language formation, cascading and search processes, and the derivation of the Maxwell-Boltzmann distribution equivalent for inelastically colliding particles in a box.