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Where does the statistics of complex systems come from? Stefan Turner
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Where Does the Statistics of Complex Systems Come From?
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- 1 Where does the statistics of complex systems come from? Stefan Turner
- 2 Relaxation processes are sample space reducing
- 3 Example: History-dependent SSR processes
- 4 Sentence-formation is SSR
- 5 SSR lead to exact Zipf's law!
- 6 Proof
- 7 What if restart SSR before it is fully relaxed?
- 8 Driven SSR
- 9 History-dependent processes with fast driving
- 10 SSR-based Zipf law is extremely robust
- 11 SSR lead to exact Zipf's law!
- 12 prior probabilities are practically irrelevant!
- 13 Zipf-law is extremely robust-accelerated SSR
- 14 SSR and diffusion on networks
- 15 SSR is a random walk on directed ordered NW
- 16 SSR = targeted random walk on networks
- 17 All diffusion processes on DAG are SSR
- 18 What happens if introduce weights on links?
- 19 What happens if we introduce cycles?
- 20 Zipf's law is an immense attractor
- 21 Conservation laws in SSR processes
- 22 Complex systems are driven non-equilibrium
- 23 Where do all the distributions come from? - Assume that driving rate depends on state 1i b
- 24 Special cases Ax = -x4, log px
- 25 Driving determines statistics of driven systems
- 26 Examples that are of SSR-nature
- 27 Conclusions
- 28 More power laws ...
