Method for Generating Long-Range Correlations for Large Systems

Abstract

We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We apply the algorithm to generate enhanced diffusion, isotropic and anisotropic self-affine surfaces, and isotropic and anisotropic correlated percolation.

4 pages, REVTEX, figures available upon request from [email protected]

Cited by in corpus (123)

• Multifractal detrended fluctuation analysis of nonstationary time series
• Detecting Long-range Correlations with Detrended Fluctuation Analysis
• Effect of Trends on Detrended Fluctuation Analysis
• Effect of nonstationarities on detrended fluctuation analysis
• Stochastic models which separate fractal dimension and Hurst effect
• Multifractal analysis of financial markets
• Comparison of detrending methods for fluctuation analysis
• Scale Invariance in the Nonstationarity of Physiological Signals
• Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques
• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• Modeling Urban Growth Patterns with Correlated Percolation
• Description of stochastic and chaotic series using visibility graphs
• Effect of nonlinear filters on detrended fluctuation analysis
• Time series irreversibility: a visibility graph approach
• Diffusion on a solid surface: Anomalous is normal
• Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series
• Scaling detection in time series: diffusion entropy analysis
• Recent advances and open challenges in percolation
• On the Role of Global Warming on the Statistics of Record-Breaking Temperatures
• Effect of extreme data loss on long-range correlated and anti-correlated signals quantified by detrended fluctuation analysis
• Fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age: A new mechanistic picture of cardiac control in healthy elderly
• From subdiffusion to superdiffusion of particles on solid surfaces
• Communication activity in a social network: relation between long-term correlations and inter-event clustering
• Vibrational excitations in systems with correlated disorder
• Persistence in Complex Systems
• Localization-delocalization transition in a one-dimensional system with long-range correlated off-diagonal disorder
• Indication of multiscaling in the volatility return intervals of stock markets
• Heuristic Segmentation of a Nonstationary Time Series
• Volatility of Linear and Nonlinear Time Series
• Percolation with long-range correlated disorder
• Study of Percolative Transitions with First-Order Characteristics in the Context of CMR Manganites
• Fractional Brownian motion with a reflecting wall
• On the multifractal effects generated by monofractal signals
• Quantitative approach to multifractality induced by correlations and broad distribution of data
• Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time series analysis
• Anderson Localization in 1D Systems with Correlated Disorder
• On the scaling ranges of detrended fluctuation analysis for long-memory correlated short series of data
• Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects
• Reflected fractional Brownian motion in one and higher dimensions
• Fracturing ranked surfaces
• Generation of short and long range temporal correlated noises
• Quantum glass phases in the disordered Bose-Hubbard model
• Site-diluted three dimensional Ising Model with long-range correlated disorder
• Predictability of real temporal networks
• Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals
• Percolation properties in a traffic model
• Effects of polynomial trends on detrending moving average analysis
• Optimal path cracks in correlated and uncorrelated lattices
• Probability density of the fractional Langevin equation with reflecting walls
• Disorder promotes ferromagnetism: Rounding of the quantum phase transition in Sr_{1-x}Ca_xRuO_3
• Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations
• Scaling Relations for Watersheds
• Competition between Two Kinds of Correlations in Literary Texts
• Microwave realization of quasi one-dimensional systems with correlated disorder
• The long-term millimeter activity of active galactic nuclei
• Correlations in magnitude series to assess nonlinearities: application to multifractal models and heartbeat fluctuations
• Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder
• Generation of Correlated Binary Sequence from White Noise
• Fermi Arcs in the Superconducting Clustered State for Underdoped Cuprates
• Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition
• Complex Network Approach to Fractional Time Series
• Fractal analysis of Sampled Profiles: Systematic Study
• Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder
• Distribution of Return Intervals of Extreme Events
• From invasion percolation to flow in rock fracture networks
• Critical behavior of the Random-Field Ising Magnet with long range correlated disorder
• Faceted patterns and anomalous surface roughening driven by long-term correlated noise
• Statistics of the critical percolation backbone with spatial long-range correlations
• Unzipping of DNA with correlated base-sequence
• Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder
• On the stability of traffic breakup patterns in urban networks
• Probability distributions for directed polymers in random media with correlated noise
• Metallic phase of disordered graphene superlattices with long-range correlations
• Transition of multi-diffusive states in a biased periodic potential
• Memory and long-range correlations in chess games
• Decomposition of Heartbeat Time Series: Scaling Analysis of the Sign Sequence
• Communication activity in social networks: growth and correlations
• Non-Local Product Rules for Percolation
• Memory functions and Correlations in Additive Binary Markov Chains
• Enhanced rare region effects in the contact process with long-range correlated disorder
• Extinction transitions in correlated external noise
• Correlation-Strength Driven Anderson Metal-Insulator Transition
• Analysis of fractional Gaussian noises using level crossing method
• The influence of statistical properties of Fourier coefficients on random surfaces
• Fluctuation analysis of high frequency electric power load in the Czech Republic
• Non-Gaussian behavior of reflected fractional Brownian motion
• Probability density of fractional Brownian motion and the fractional Langevin equation with absorbing walls
• Inferring long memory using extreme events
• Breaking universality in random sequential adsorption on a square lattice with long-range correlated defects
• The Role of Power-Law Correlated Disorder in the Anderson Metal-Insulator Transition
• Disorder correlations at smeared phase transitions
• Retention capacity of correlated surfaces
• Ordering Behavior of the Two-Dimensional Ising Spin Glass with Long-Range Correlated Disorder
• Scaling laws for random walks in long-range correlated disordered media
• Cellular Fourier analysis for geometrically disordered materials
• Critical exponent $\nu$ of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques
• Crossing Statistics of Anisotropic Stochastic Surface
• Nonlinear Correlations in Multifractals: Visibility Graphs of Magnitude and Sign Series
• Records in Fractal Stochastic Processes
• A Fast Algorithm for Generating Long Self-Affine Profiles
• Critical properties of the Susceptible-Exposed-Infected model with correlated temporal disorder
• Dual-induced multifractality in online viewing activity
• Scaling Properties of Urban Facilities
• Anderson localization in optical lattices with speckle disorder
• Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: Effect of disorder correlations
• Correlation properties of the random linear high-order Markov chains
• Appropriateness of correlated first order auto-regressive processes for modeling daily temperature records
• Bunches of Random Cross-correlated Sequences
• Entropic analysis of the localization-delocalization transition in a one-dimensional correlated lattice
• Qualitative Assessment of Gene Expression in Affymetrix Genechip Arrays
• Fractional Brownian motion with mean-density interaction: a myopic self-avoiding fractional stochastic process
• Percolation of systems having hyperuniformity or giant number-fluctuations
• Effects of Long-Range Correlations in Random-Mass Dirac Fermions
• Phase transitions and continuously variable scaling in a chiral quenched disordered model
• Fractality of eroded coastlines of correlated landscapes
• Learning and generation of long-range correlated sequences
• Generation of hierarchically correlated multivariate symbolic sequences
• First Passage Time Statistics For Systems Driven by Long Range Gaussian Noises
• Quantum Spin Chains with Nonlocally-Correlated Random Exchange Coupling and Random-Mass Dirac Fermions
• Statistics of Extreme Values in Time Series with Intermediate-Term Correlations
• Temperature scaling analysis of the 3D disordered Ising model with power-law correlated defects
• Tempered fractional Brownian motion on finite intervals
• On the Scale free laws of Urban Facilities