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From Riemann zeta through L-functions, random matrices, quantum chaos, brownian diffusion, critical collective phenomena ... to financial correlations

Ryszard Wojnar 

Polish Academy of Sciences, Institute of Fundamental Technological Research (IPPT PAN), Świętokrzyska 21, Warszawa 00-049, Poland

Abstract

Computations of 1013 zeros of zeta function and many primes are the richest source of the best data to study important correlations.
May be the power of visual and audible perception with use of animation and sound musical sequences could help to reveal some laws common to similar correlations in random matrices and in financial fluctuations.
L-function closest to Riemann zeta may permit to analyse the simplest model of crystallization. Similarity of correlation in random matrix eigenvalues to financial correlations indicates a possible analogy between stock price fluctuations, brownian diffusion and critical collective phenomena [1].

[1] H. E. Stanley et al., Self-organized complexity in economics and finance, Proc. Natl. Acad. Sci. 99-Supp, 2561-2565 (2002).

 

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Related papers

Presentation: oral at Symposium on Econo- and Sociophysics 2004, by Ryszard Wojnar
See On-line Journal of Symposium on Econo- and Sociophysics 2004

Submitted: 2004-10-29 19:54
Revised:   2009-06-08 12:55