Maximum of the characteristic polynomial of random unitary matrices

DOI10.1007/s00220-016-2740-6zbMath1371.15036arXiv1511.07399OpenAlexW3104709962MaRDI QIDQ507178

Louis-Pierre Arguin, David Belius, Paul Bourgade

Publication date: 3 February 2017

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07399

zbMATH Keywords

circular unitary ensembleRiemann-Hilbert problemsToeplitz determinantsextreme value statisticsFisher-Hartwig singularitiesrandom unitary matrices

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Extreme value theory; extremal stochastic processes (60G70) Random matrices (algebraic aspects) (15B52)

Related Items

On the moments of the partition function of the \(C\beta E\) field ⋮ Maxima of branching random walks with piecewise constant variance ⋮ Maximum and coupling of the sine-Gordon field ⋮ Asymptotics of Muttalib-Borodin determinants with Fisher-Hartwig singularities ⋮ Random Hermitian matrices and Gaussian multiplicative chaos ⋮ On the extreme values of the Riemann zeta function on random intervals of the critical line ⋮ Extreme gaps between eigenvalues of Wigner matrices ⋮ Maxima of log-correlated fields: some recent developments* ⋮ Global rigidity and exponential moments for soft and hard edge point processes ⋮ Subcritical multiplicative chaos for regularized counting statistics from random matrix theory ⋮ Extending the characteristic polynomial for characterization of C\(_{20}\) fullerene congeners ⋮ Imaginary multiplicative chaos: moments, regularity and connections to the Ising model ⋮ Uniform asymptotics of Toeplitz determinants with Fisher-Hartwig singularities ⋮ Large gap asymptotics for Airy kernel determinants with discontinuities ⋮ The Fyodorov-Bouchaud formula and Liouville conformal field theory ⋮ The distribution of overlaps between eigenvectors of Ginibre matrices ⋮ A CLT for the characteristic polynomial of random Jacobi matrices, and the G\(\beta\)E ⋮ Extreme value statistics of correlated random variables: a pedagogical review ⋮ Upper bounds for the maximum deviation of the Pearcey process ⋮ Multiscale coupling and the maximum of \(\mathcal{P}(\phi)_2\) models on the torus ⋮ Large N two-dimensional Yang–Mills fields for the spectral behavior of Brownian particles and relativistic many-body systems ⋮ Voting models and semilinear parabolic equations ⋮ Strong approximation of Gaussian \(\beta\) ensemble characteristic polynomials: the hyperbolic regime ⋮ On the moments of moments of random matrices and Ehrhart polynomials ⋮ Maximum of the characteristic polynomial of the Ginibre ensemble ⋮ Extremal statistics of quadratic forms of GOE/GUE eigenvectors ⋮ Law of large numbers for the maximum of the two-dimensional Coulomb gas potential ⋮ Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Convergence of the maximum in the regime of weak correlations ⋮ On the generating function of the Pearcey process ⋮ Secular coefficients and the holomorphic multiplicative chaos ⋮ Universality of the minimum modulus for random trigonometric polynomials ⋮ Multiplicative chaos and the characteristic polynomial of the CUE: The 𝐿¹-phase ⋮ Rigidity of eigenvalues for \(\beta\) ensemble in multi-cut regime ⋮ On the rightmost eigenvalue of non-Hermitian random matrices ⋮ The distribution of values of zeta and \(L\)-functions ⋮ On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices ⋮ Maximum of the Ginzburg-Landau fields ⋮ The Riemann zeta function and Gaussian multiplicative chaos: statistics on the critical line ⋮ The phase diagram of the complex branching Brownian motion energy model ⋮ High points of branching Brownian motion and McKean's Martingale in the Bovier-Hartung extremal process ⋮ Extreme values of CUE characteristic polynomials: a numerical study ⋮ The law of large numbers for the maximum of almost Gaussian log-correlated fields coming from random matrices ⋮ Moments of moments and branching random walks ⋮ Band-limited mimicry of point processes by point processes supported on a lattice ⋮ On the maximum of the C\(\beta\)E field ⋮ The maximum deviation of the \(\mathrm{sine}_\beta\) counting process ⋮ Gaussian fluctuations of the determinant of Wigner matrices ⋮ Geometry of the Gibbs measure for the discrete 2D Gaussian free field with scale-dependent variance ⋮ How much can the eigenvalues of a random Hermitian matrix fluctuate? ⋮ Mesoscopic central limit theorem for the circular \(\beta\)-ensembles and applications ⋮ Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Extremal process in the weakly correlated regime ⋮ A sharp rate of convergence for the empirical spectral measure of a random unitary matrix ⋮ Moments of the Riemann zeta function on short intervals of the critical line ⋮ A simple backward construction of branching Brownian motion with large displacement and applications ⋮ On the moments of the moments of the characteristic polynomials of random unitary matrices ⋮ The hard-to-soft edge transition: exponential moments, central limit theorems and rigidity ⋮ On Cramér-von Mises statistic for the spectral distribution of random matrices ⋮ Hierarchical structure in the trace formula* ⋮ Optimal local law and central limit theorem for \(\beta\)-ensembles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional Brownian motion with Hurst index \({H = 0}\) and the Gaussian unitary ensemble
• Extreme gaps between eigenvalues of random matrices
• Convergence in law of the minimum of a branching random walk
• Extreme values for two-dimensional discrete Gaussian free field
• Gaussian multiplicative chaos and applications: a review
• Convergence in law of the maximum of nonlattice branching random walk
• The subleading order of two dimensional cover times
• Maxima of a randomized Riemann zeta function, and branching random walks
• Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
• Rigidity of eigenvalues of generalized Wigner matrices
• Convergence of the centered maximum of log-correlated Gaussian fields
• Mesoscopic fluctuations of the zeta zeros
• Bounds for the Stieltjes transform and the density of states of Wigner matrices
• The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos -- the \(L^2\)-phase
• Maximum of a log-correlated Gaussian field
• Toeplitz determinants with merging singularities
• Tightness for a family of recursion equations
• Spectral functions, special functions and the Selberg zeta function
• Derrida's generalized random energy models. II: Models with continuous hierarchies
• Cover times for Brownian motion and random walks in two dimensions
• Entropic repulsion and the maximum of the two-dimensional harmonic crystal.
• Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal \(1/f\) noise
• Polymers on disordered trees, spin glasses, and traveling waves.
• Minima in branching random walks
• Poisson-Dirichlet statistics for the extremes of a log-correlated Gaussian field
• Poisson-Dirichlet statistics for the extremes of the two-dimensional discrete Gaussian free field
• Extreme local extrema of two-dimensional discrete Gaussian free field
• Linear functionals of eigenvalues of random matrices
• Derrida’s Random Energy Models
• On the distribution of the maximum value of the characteristic polynomial of GUE random matrices
• Freezing transitions and extreme values: random matrix theory, and disordered landscapes
• Tightness of the recentered maximum of the two-dimensional discrete Gaussian free field
• On the asymptotics of a Toeplitz determinant with singularities
• Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle
• Convergence in Law of the Maximum of the Two‐Dimensional Discrete Gaussian Free Field
• Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential
• Maximal displacement of branching brownian motion
• On the Eigenvalues of Random Matrices
• Limit theorems for the minimal position in a branching random walk with independent logconcave displacements
• Statistical mechanics of logarithmic REM: duality, freezing and extreme value statistics of 1/fnoises generated by Gaussian free fields
• Random matrix theory and \(\zeta(1/2+it)\).
• On the characteristic polynomial of a random unitary matrix