Fractional Brownian motion with Hurst index \({H = 0}\) and the Gaussian unitary ensemble

DOI10.1214/15-AOP1039zbMath1393.60037arXiv1312.0212MaRDI QIDQ317494

Boris. A. Khoruzhenko, Nicholas J. Simm, Yan. V. Fyodorov

Publication date: 30 September 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.0212

zbMATH Keywords

fractional Brownian motionrandom matrix theorygeneralized processeslogarithmically correlatedmesoscopic regime

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Random matrices (probabilistic aspects) (60B20) Functional limit theorems; invariance principles (60F17) Prediction theory (aspects of stochastic processes) (60G25)

Related Items (39)

Random matrices with merging singularities and the Painlevé V equation ⋮ Random Hermitian matrices and Gaussian multiplicative chaos ⋮ Mesoscopic central limit theorem for general \(\beta\)-ensembles ⋮ Global fluctuations for 1D log-gas dynamics. Covariance kernel and support ⋮ Subcritical multiplicative chaos for regularized counting statistics from random matrix theory ⋮ Moments of the position of the maximum for GUE characteristic polynomials and for log-correlated Gaussian processes ⋮ Gaussian and non-Gaussian fluctuations for mesoscopic linear statistics in determinantal processes ⋮ On Barnes beta distributions and applications to the maximum distribution of the 2D Gaussian free field ⋮ Imaginary multiplicative chaos: moments, regularity and connections to the Ising model ⋮ The multiplicative chaos of \(H=0\) fractional Brownian fields ⋮ From rough to multifractal volatility: the log S-fBm model ⋮ A characterisation of the Gaussian free field ⋮ A CLT for the characteristic polynomial of random Jacobi matrices, and the G\(\beta\)E ⋮ Local scaling limits of Lévy driven fractional random fields ⋮ Limit theorems on the mesoscopic scale for the Anderson model ⋮ The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles ⋮ Optimal stopping with signatures ⋮ Gaussian multiplicative chaos for Gaussian orthogonal and symplectic ensembles ⋮ The random normal matrix model: insertion of a point charge ⋮ Testing in high-dimensional spiked models ⋮ Secular coefficients and the holomorphic multiplicative chaos ⋮ Multiplicative chaos and the characteristic polynomial of the CUE: The 𝐿¹-phase ⋮ Central limit theorems for the real eigenvalues of large Gaussian random matrices ⋮ Mod-Gaussian convergence for random determinants ⋮ 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 ⋮ On Mesoscopic Equilibrium for Linear Statistics in Dyson’s Brownian Motion ⋮ Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint ⋮ Mesoscopic fluctuations for unitary invariant ensembles ⋮ Rigidity and a mesoscopic central limit theorem for Dyson Brownian motion for general \(\beta\) and potentials ⋮ How much can the eigenvalues of a random Hermitian matrix fluctuate? ⋮ On fluctuations of global and mesoscopic linear statistics of generalized Wigner matrices ⋮ Comparing the stochastic nonlinear wave and heat equations: a case study ⋮ A review of conjectured laws of total mass of Bacry–Muzy GMC measures on the interval and circle and their applications ⋮ Third-order phase transition: random matrices and screened Coulomb gas with hard walls ⋮ On the moments of the moments of the characteristic polynomials of random unitary matrices ⋮ On Cramér-von Mises statistic for the spectral distribution of random matrices ⋮ Universality of mesoscopic fluctuations for orthogonal polynomial ensembles

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Universality of mesoscopic fluctuations for orthogonal polynomial ensembles
• Random conformal weldings
• Gaussian multiplicative chaos and applications: a review
• Exact solution of the six-vertex model with domain wall boundary conditions. Disordered phase
• Stochastic calculus for fractional Brownian motion with Hurst exponent \(H>\frac 1 4 \): A rough path method by analytic extension
• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• The isomonodromy approach to matrix models in 2D quantum gravity
• Log-infinitely divisible multifractal processes
• Universality for eigenvalue correlations at the origin of the spectrum
• Gaussian fluctuations of eigenvalues in the GUE
• The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal \(1/f\) noise
• Analyticity of the planar limit of a matrix model
• On fluctuations of eigenvalues of random Hermitian matrices.
• The Altshuler-Shklovskii formulas for random band matrices. II: The general case
• Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant
• Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices
• The Altshuler-Shklovskii formulas for random band matrices. I: The unimodular case
• Gaussian free fields for mathematicians
• Lectures on Random Matrix Models
• Freezing transitions and extreme values: random matrix theory, and disordered landscapes
• General β-Jacobi Corners Process and the Gaussian Free Field
• Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential
• An Introduction to Random Matrices
• A limit theorem for measurable random processes and its applications
• On the Eigenvalues of Random Matrices
• Asymptotic distribution of smoothed eigenvalue density. II. Wigner random matrices
• Asymptotic distribution of smoothed eigenvalue density. I. Gaussian random matrices
• The Noise in the Circular Law and the Gaussian Free Field
• Long Range Dependence
• Fractional Brownian Motions, Fractional Noises and Applications
• Random matrix theory and \(\zeta(1/2+it)\).
• On the characteristic polynomial of a random unitary matrix

This page was built for publication: Fractional Brownian motion with Hurst index \({H = 0}\) and the Gaussian unitary ensemble