1. Patterns Embedded In Time Series By Means Of RMT
Huijie Yang (杨会杰)
Biz School
University of Shanghai for Science and Technology
Jungong Rd#516,Shanghai,
Date: June 3, 2011
Add.: Biz School USST

2. Random Matrix Theory
中国科学技术大学 顾雁

3. Statistics of Nuclear Levels/spectra
Neutron scattering
NNLS distribution

4. 2. It is too complicated to be dealt with in detail.
Hence,it can be dealt with in a simple way,
The Hamiltonian of a complex quantum system

5. 2. Some concepts
本征值分布
本征值间隔分布

6. 谱刚度
量子混沌
Classical system:
Chaos, regular
Quantum system:
Brody, Poisson

7. Localization and extension state
Disorder induced localization

8. Tight-binding Hamiltonian
1) regular lattice: extension
2) Disorder lattice: localized state

9. 3) What about aperiodic lattice? MULTIFRACTAL
Power-law

10. Ideas Map time series to 1-dimensional disorder lattice
by series element to site energy
Structure of the lattice determines the characteristics of
The waves on the lattice
Characteristics of the wave on the lattice
Can be used to Measure the structures of the series

11. time series
where
The site energies in 1-D lattice

12. Hopping integral
Unfolding procedure:

13. 1. RMT for Fractional Brownian Motion (FBM) series
Some Results
1. RMT for Fractional Brownian Motion (FBM) series
shuffling

14. Hurst exponents for the NNLS series
H and H’ are uncorrelated: A new kind of fractal

15. q in the Brody distribution
q-1 : Wigner distribution
Non-distinguishable

16. Chaotic series
1 Logistic.
Fractals for
NNLS series

18. Conclusions Series analysis ---Anderson localizations For FBM series,
new fractals
NNLS distribution are non-distinguishable
For Chaos series,
NNLS distribution are consistent
with Lyapunov exponent
4. Advantages:
Physical picture;
Use condensed mater theories

19. Thanks for your helpful comments Contributors Lily Zhao from USST
Guimei Zhu from NUS
Jie Ren from NUS
Thanks for your
helpful comments