相关论文: Correlation Functions, Cluster Functions and Spaci…
We study the behavior of two-time correlation functions at late times for finite system sizes considering observables whose (one-point) average value does not depend on energy. In the long time limit, we show that such correlation functions…
The simplest examples of chaotic maps are linear, area-preserving maps on the circle, torus, or product of tori; respectively known as the Bernoulli map, the cat map, and the recently introduced "spatiotemporal" cat map. We study…
Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…
We investigate the distribution of clusters of galaxies and determine the cluster correlation function and power spectrum. Clusters of galaxies located in rich superclusters with at least 8 members form a quasiregular network of…
Cosmological correlation functions are significantly more complex than their flat-space analogues, such as tree-level scattering amplitudes. While these amplitudes have simple analytic structure and clear factorisation properties,…
The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the…
We present conjectured exact expressions for two types of correlations in the dense O$(n=1)$ loop model on $L\times \infty$ square lattices with periodic boundary conditions. These are the probability that a point is surrounded by $m$ loops…
In Random Matrix Theory the local correlations of the Laguerre and Jacobi Unitary Ensemble in the hard edge scaling limit can be described in terms of the Bessel kernel (containing a parameter $\alpha$). In particular, the so-called hard…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation…
Nuclear parton distributions and structure functions are determined in an effective chiral quark theory. We also discuss an extension of our model to fragmentation functions.
The zeros of semi-orthogonal functions with respect to a probability measure mu supported on the unit circle can be applied to obtain Szego quadrature formulas. The discrete measures generated by these formulas weakly converge to the…
We reconsider the inference of spatial power spectra from angular clustering data and show how to include correlations in both the angular correlation function and the spatial power spectrum. Inclusion of the full covariance matrices…
Non-Hermitian random matrices with symplectic symmetry provide examples for Pfaffian point processes in the complex plane. These point processes are characterised by a matrix valued kernel of skew-orthogonal polynomials. We develop their…
We undertake an analysis of Fredholm determinants arising from kernels whose defining functions satisfy a Schr\"odinger type equation. When this defining function is the Airy one, the evaluation of the corresponding Fredholm determinant…
This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
Introduced by Okounkov and Reshetikhin, the Schur process is known to be a determinantal point process, meaning that its correlation functions are minors of a single correlation kernel matrix. Previously, this was derived using…
We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for the generating function, we re-obtain several well-known kernels from random matrix…