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Complex system; scale invariance; stochastic processes; cascade; records.

The purpose of this review paper is to summarize progress on a recently introduced topic: Sample space reducing (SSR) stochastic processes. The concept of SSR has been coined to offer an alternative route that can explain the origin of power law features associated with complex systems. Understanding the emergence of scale-free behavior remains a topic of continuing interest, specially in the statistical physics community, due to its appearance in diverse systems, besides the existence of different explanations. One crucial aspect of theSSR is that the problem can be solved analytically. This develops the topic even more attracting and offers a possibility to provide a deeper understanding. Eventually numerous generalization of the SSR has been advanced,and a shift in the focus was also seen from the scale-free statistics to different physically relevant forms. We here primarily discuss the following points: (i) Various ways to visualize the SSR and its applications, (ii) mention, fora comparison, other mechanisms that reveal the origin of the power law distribution, (iii) different generalizations with their importance and (iv) a brief discussion with future perspectives.

AVINASH CHAND YADAV¹

1. Department of Physics and Astronomical Sciences, Central University of Jammu, Samba 181 143, India

Published

16 September 2019