We study multifractal spectra of critical wave functions at the integer quantum Hall plateau transition using the Chalker-Coddington network model. Our numerical results provide important new constraints which any critical theory for the transition will have to satisfy. We find a nonparabolic multifractal spectrum and determine the ratio of boundary to bulk multifractal exponents. Our results r...

We investigate the statistical anisotropy and gaussianity of temperature fluctuations of Cosmic Microwave Background (CMB) radiation data from the Wilkinson Microwave Anisotropy Probe survey, using the Multifractal Detrended Fluctuation Analysis, Rescaled Range, and Scaled Windowed Variance methods. Multifractal Detrended Fluctuation Analysis shows that CMB fluctuations has a long-range correla...

Multifractal analysis has become a reference tool for signal and image processing. Grounded in the quantification of local regularity fluctuations, it proven useful an increasing range applications, yet so far involving only univariate data (scalar valued time series or single channel images). Recently theoretical ground multivariate multifractal been devised, showing potential quantifying tran...

This is a short review in honor of B. Mandelbrot’s 80st birthday, to appear in Wilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial time series, in particular the intermittent, long-memory nature of the volatility. We describe in details the Bacry-Muzy-Delour multifractal random walk. We poi...

We describe the main features of wavelet techniques in multifractal analysis, using wavelet bases both as a tool for analysis, and for synthesis. We focus on two promising developments: On the analysis side, we introduce the quantile leader method, which allows to put into light nonconcave multifractal spectra; on the synthesis side, we study some extensions of random wavelet series which allow...

Abstract. Some asymptotic properties of a Brownian motion in multifractal time, also called multifractal random walk, are established. We show the almost sure and L convergence of its structure function. This is an issue directly connected to the scale invariance and multifractal property of the sample paths. We place ourselves in a mixed asymptotic setting where both the observation length and...

The design of appropriate multifractal analysis algorithms, able to correctly characterize the scaling properties of multifractal systems from experimental, discretized data, is a major challenge in the study of such scale invariant systems. In the recent years, a growing interest for the application of the microcanonical formalism has taken place, as it allows a precise localization of the fra...

Physical variables in scale invariant systems often show chaotic, turbulent-like behaviour, what is commonly associated to the existence of a fractal or multifractal underlying structure. The detection of such structure over experimental data requires appropriate methods of analysis and to establish criteria to measure the confidence degree in the estimates. In this paper we will test four diff...