Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal \(1/f\) noise

DOI10.1007/s10955-012-0623-6zbMath1260.82016arXiv1207.4614OpenAlexW3102552442WikidataQ62415879 ScholiaQ62415879MaRDI QIDQ1938799

Alberto Rosso, Pierre Le Doussal, Yan. V. Fyodorov

Publication date: 25 February 2013

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4614

zbMATH Keywords

extreme valuesmultifractalsrandom energy model\(1/f\) noiselogarithmically correlated random fields

Mathematics Subject Classification ID

Random fields (60G60) Extreme value theory; extremal stochastic processes (60G70) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Fractals (28A80)

Related Items

The largest fragment of a homogeneous fragmentation process ⋮ Moments of the position of the maximum for GUE characteristic polynomials and for log-correlated Gaussian processes ⋮ Fractional Brownian motion with Hurst index \({H = 0}\) and the Gaussian unitary ensemble ⋮ On Barnes beta distributions and applications to the maximum distribution of the 2D Gaussian free field ⋮ Freezing transitions and extreme values: random matrix theory, and disordered landscapes ⋮ Extreme value statistics of correlated random variables: a pedagogical review ⋮ Towards rigorous analysis of the Levitov–Mirlin–Evers recursion ⋮ Extreme values of CUE characteristic polynomials: a numerical study ⋮ A theory of intermittency differentiation of 1D infinitely divisible multiplicative chaos measures ⋮ Maximum of the characteristic polynomial of random unitary matrices ⋮ Freezing and decorated Poisson point processes ⋮ High values of disorder-generated multifractals and logarithmically correlated processes ⋮ How much can the eigenvalues of a random Hermitian matrix fluctuate? ⋮ Derrida’s Random Energy Models ⋮ A review of conjectured laws of total mass of Bacry–Muzy GMC measures on the interval and circle and their applications ⋮ Log-correlated large-deviation statistics governing Huygens fronts in turbulence

Cites Work

• Random conformal weldings
• Critical Gaussian multiplicative chaos: convergence of the derivative martingale
• Negative fractal dimensions and multifractals
• Mellin transform of the limit lognormal distribution
• Continuous cascade models for asset returns
• Nonconcave entropies in multifractals and the thermodynamic formalism
• Random curves by conformal welding
• Amplitude truncation of Gaussian \(1/f^{\alpha }\) noises
• Multifractal dimensions for branched growth
• Log-infinitely divisible multifractal processes
• Entropic repulsion and the maximum of the two-dimensional harmonic crystal.
• Polymers on disordered trees, spin glasses, and traveling waves.
• Extremes of the discrete two-dimensional Gaussian free field
• ON THE STOCHASTIC DEPENDENCE STRUCTURE OF THE LIMIT LOGNORMAL PROCESS
• Tightness of the recentered maximum of the two-dimensional discrete Gaussian free field
• Random-energy model: An exactly solvable model of disordered systems
• Critical curves in conformally invariant statistical systems
• Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential
• Multifractal Cascade Dynamics and Turbulent Intermittency
• Multifractals, operator-product expansion, and field theory
• Conformally Invariant Fractals and Potential Theory
• Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules
• The multifractal nature of turbulent energy dissipation
• Modelling financial time series using multifractal random walks

This page was built for publication: Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal \(1/f\) noise