相关论文: Summing graphs for random band matrices

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as…

Topology is a central notion in the classification of band insulators and characterization of entangled many-body quantum states. In some cases, it manifests as quantized observables such as quantum Hall conductance. However, being…

Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of…

We consider independent long-range percolation models on locally finite vertex-transitive graphs. Using coupling ideas we prove strict monotonicity of the critical points with respect to local perturbations in the connection function,…

We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…

We study the spectral function of the 2D Hubbard model using cluster perturbation theory, and the density matrix renormalization group as a cluster solver. We reconstruct the two-dimensional dispersion at, and away from half-filling using…

We describe the distribution of the first finite number of eigenvalues in a newly-forming band of the spectrum of the random Hermitean matrix model. The method is rigorously based on the Riemann-Hilbert analysis of the corresponding…

We use two variational techniques to prove upper bounds for sums of the lowest several eigenvalues of matrices associated with finite, simple, combinatorial graphs. These include estimates for the adjacency matrix of a graph and for both…

Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions…

The ground state properties of $N$ spinless free fermions in a $d$-dimensional confining potential are studied. We find that any $n$-point correlation function has a simple determinantal structure that allows us to compute several…

A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…

The generalized tight-binding model, with the exact diagonalization method, is developed to investigate optical properties of graphene in five kinds of external fields. The quite large Hamiltonian matrix is transferred into the band-like…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…

Convenient Cutkosky-like diagrammatic rules for computing the spectral densities of arbitrary two-point correlation functions in finite temperature field theory are derived. The approach is based on an explicit analytic continuation of…

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…

Layers of two-dimensional materials arranged at a twist angle with respect to each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states.…

Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…

The paper continues previous works which study the behavior of second correlation function of characteristic polynomials of the special case of $n\times n$ one-dimensional Gaussian Hermitian random band matrices, when the covariance of the…