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Where does the statistics of complex systems come from? Stefan Turner
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Relaxation processes are sample space reducing
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Example: History-dependent SSR processes
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Sentence-formation is SSR
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SSR lead to exact Zipf's law!
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Proof
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What if restart SSR before it is fully relaxed?
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Driven SSR
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History-dependent processes with fast driving
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SSR-based Zipf law is extremely robust
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SSR lead to exact Zipf's law!
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prior probabilities are practically irrelevant!
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Zipf-law is extremely robust-accelerated SSR
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SSR and diffusion on networks
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SSR is a random walk on directed ordered NW
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SSR = targeted random walk on networks
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All diffusion processes on DAG are SSR
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What happens if introduce weights on links?
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What happens if we introduce cycles?
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Zipf's law is an immense attractor
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Conservation laws in SSR processes
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Complex systems are driven non-equilibrium
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Where do all the distributions come from? - Assume that driving rate depends on state 1i b
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Special cases Ax = -x4, log px
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Driving determines statistics of driven systems
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Examples that are of SSR-nature
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Conclusions
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More power laws ...
Description:
Explore the origins of complex systems statistics in this comprehensive lecture by Stefan Thurner at the International Centre for Theoretical Sciences. Delve into sample space reducing (SSR) processes and their connection to Zipf's law, examining applications in sentence formation, network diffusion, and driven non-equilibrium systems. Learn about the robustness of Zipf's law, conservation laws in SSR processes, and the role of driving rates in determining system statistics. Gain insights into various examples of SSR-nature phenomena and their implications for understanding complex systems across multiple disciplines.

Where Does the Statistics of Complex Systems Come From?

International Centre for Theoretical Sciences
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Where does the statistics of complex systems come from? Stefan Turner