Spectral fluctuation characterization of random matrix ensembles through wavelets

Manimaran, P.; Lakshmi, P. Anantha; Panigrahi, Prasanta K.

doi:10.1088/0305-4470/39/42/l02

Cited by 15 publications

(17 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The α dfa exponent has been applied previously to explore the statistical self-similarity in the quantum spectrum, RMT, and in the atomic spectra in Refs. [13,23]. These exponents can be related using the expressions α dfa = (β ps + 1)/2 [22], and at the same time these exponents can be related with η emd through the relation α dfa = 1 + η emd /2 [4].…”

Section: Comparison With Other Techniquesmentioning

confidence: 99%

Manifestation of scale invariance in the spectral fluctuations of random matrices

et al. 2013

View full text Add to dashboard Cite

We apply the Empirical Mode Decomposition method to extract intrinsic modes in the fluctuations of the spectra of random matrices. The hierarchy of the modes follows a power law with an exponent that changes smoothly in the whole range of the transition from the Gaussian orthogonal to the Gaussian diagonal ensemble. This property of scale invariance represents a new quantification of quantum chaos in systems that are characterized by the statistics of Random Matrix Theory.

show abstract

Section: Comparison With Other Techniquesmentioning

confidence: 99%

Manifestation of scale invariance in the spectral fluctuations of random matrices

et al. 2013

View full text Add to dashboard Cite

show abstract

“…We observe the transient and bursty behavior at different levels of analysis which were not apparent from the NLR. The discrete wavelet based method to characterize multifractality proposed by Manimaran et al [8,9], has been successfully applied to extract multifractality of various time series [10,11,19]. In this procedure, we use the normalized log returns obtained through Eq(15) to obtain the time series profile by taking a cumulative sum of the normalized returns:…”

Section: Wavelet Based Fluctuation Extraction and Analysis And Characmentioning

confidence: 99%

Characterizing multi-scale self-similar behavior and non-statistical properties of fluctuations in financial time series

Ghosh

Manimaran

Panigrahi

2011

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

We make use of wavelet transform to study the multi-scale, self similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scales. The fact that, the wavelets belonging to the Daubechies' (Db) basis enables one to isolate local polynomial trends of different degrees, plays the key role in isolating fluctuations at different scales. One of the primary motivations of this work is to study the emergence of the k −3 behavior [1] of the fluctuations starting with high frequency fluctuations. We make use of Db4 and Db6 basis sets to respectively isolate local linear and quadratic trends at different scales in order to study the statistical characteristics of these financial time series. The fluctuations reveal fat tail non-Gaussian behavior, unstable periodic modulations, at finer scales, from which the characteristic k −3 power law behavior emerges at sufficiently large scales. We further identify stable periodic behavior through the continuous Morlet wavelet.

show abstract

“…Sophisticated methods have been invented to characterize the actual fluctuations extracted from the average behavior, and the fractal nature of non-stationary time series. These include-detrended fluctuation analysis (DFA) and its variance [22,23], the wavelet transform [24,25] based multi-resolution analysis [26,27], multifractal detrended fluctuation analysis (MFDFA) [28] etc.. DFA technique [22] was developed in order to determine minutely the presence of any long range correlation [22,29] in a non-stationary series. However, despite a multitude of real-data analyses, a proper detection of the multifractality in the experimental data still presents much difficulty and is not always reliable [30].MFDFA technique [28] is actually a generalization of standard DFA technique for the characterization of multifractal nature of a series.…”

Section: Introductionmentioning

confidence: 99%

Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

Bhoumik

Deb

Bhattacharyya

et al. 2016

Advances in High Energy Physics

View full text Add to dashboard Cite

We have studied the multifractality of pion emission process in 16 O-AgBr interactions at 2.1AGeV & 60AGeV, 12 C-AgBr & 24 Mg-AgBr interactions at 4.5AGeV and 32 S-AgBr interactions at 200AGeV using Multifractal Detrended Fluctuation Analysis (MFDFA) method which is capable of extracting the actual multifractal property filtering out the average trend of fluctuation. The analysis revels that the pseudo rapidity distribution of the shower particles is multifractal in nature for all the interactions i.e. pion production mechanism has in built multi-scale self-similarity property. We have employed MFDFA method for randomly generated events for 32 S-AgBr interactions at 200AGeV. Comparison of expt. results with those obtained from randomly generated data set reveals that the source of multifractality in our data is the presence of long range correlation. Comparing the results obtained from different interactions, it may be concluded that strength of multifractality decreases with projectile mass for same projectile energy and for a particular projectile it increases with energy. The values of ordinary Hurst exponent suggest that there is long range correlation present in our data for all the interactions. 5]. Natural systems, which have irregular pattern at different scales, exhibit fractal nature. Fractals are generally classified into two categories i) Monofractal and ii) Multifractals. For monofractals scaling properties of the system is identical throughout the system on the other hand "Multifractals" are more complicated self-similar structure that consist of a number of weighted fractals with different non-integer dimensions. As the scaling properties are dissimilar in different parts of the system, multifractal systems require at least more than one scaling exponent to describe the scaling behavior of the system [6]. Investigation of multifractality is of great importance as its origin may be associated with the presence of long range correlation in the system. Correlation study has the potential to

show abstract

Spectral fluctuation characterization of random matrix ensembles through wavelets

Cited by 15 publications

References 35 publications

Manifestation of scale invariance in the spectral fluctuations of random matrices

Manifestation of scale invariance in the spectral fluctuations of random matrices

Characterizing multi-scale self-similar behavior and non-statistical properties of fluctuations in financial time series

Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

Contact Info

Product

Resources

About