Seminar: History-dependence and emergence of scaling through Sample Space Reducing processes

DATE / VENUE ============ October 16th

ISI Red Room

11:00 a.m.


Bernat Corominas-Murtra, Research Assistant at Medical University of Vienna, Section for Science of Complex Systems.

History-dependence and emergence of scaling through Sample Space Reducing processes

The comprehension of the mechanisms behind scaling patterns has become on of the hot topics of modern statistical physics [1]. From complex networks to critical phenomena, scaling laws emerge in somewhat regular way. In this talk I will link the scaling patterns observed in many complex systems with a crucial property behind them: history-dependence [2]. Classical examples of history dependent processes with extremely interesting properties are Pólya urns, the Chinese restaurant or the recurrent random sequences proposed by Ulam and Kac. The link between history-dependence and scaling comes from the recently defined Sample Space Reducing (SSR) processes [3,4]. SSR processes connect history dependence and scaling in an extremely intuitive way. In addition, SSR process are a totally new route to scaling which can explain a huge range of power-law exponents thanks to the unique assumption that the sampling space is reduced as long as the process unfolds. Simple forms of SSR processes are regular sampling processes where the ‘left-right’ symmetry is broken, leading to a minimal form of history-dependence. In spite of the simplicity of this basic assumption, SSR processes display a wide spectrum of surprising properties. From this zoo of interesting properties, maybe the most remarkable one is the role of the scaling law known as ‘Zipf’s law’ as an attractor, which provides a new, fundamental explanation for the ubiquity of such scaling pattern in real systems. The intuitive rationale behind the SSR processes and the surprisingly simple mathematical apparatus needed to understand them makes the SSR process approach a new research area with promising applications.


[1] Newman,  M E J (2005) “Power laws, Pareto distributions and Zipf's law"  Contemporary Physics 46 (5): 323–351.

[2] Arthur, B (1994) Increasing Returns and Path Dependence in the Economy. The University of Michigan Press, Ann Arbor.

[3] Corominas-Murtra, B, Hanel, R, and Thurner, S (2015) “Understanding scaling through history-dependent processes with collapsing sample space”. Proc Nac Acad Sci USA. 112 (17) 5348–5353.

[4] Thurner, S, Hanel, R, Liu, B, and Corominas-Murtra, B (2015) “Understanding Zipf’s law of word frequencies through sample-space collapse in sentence formation”. J R Soc Interface. 12 (108).