相关论文: Spectral correlations: understanding oscillatory c…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
For many applications, critical information about system dynamics is encoded in associated eigenvalue problems that can be posed as linear Hamiltonian systems with suitable boundary conditions. Motivated by examples from hydrodynamics,…
A generalized Hubbard-Stratonovitch transformation relating an integral over random unitary N times N matrices to an integral over Efetov's unitary sigma model manifold, is introduced. This transformation adapts the supersymmetry method to…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain…
Arrangement graphs were introduced for their connection to computational networks and have since generated considerable interest in the literature. In a pair of recent articles by Chen, Ghorbani and Wong, the eigenvalues for the adjacency…
Let $A$ be a closed symmetric operator with the deficiency index $(p,p)$, $p<\infty$, acting in a Hilbert space $\sH$ and let $\sL$ be a subspace of $\sH$. The set of $\sL$-resolvents of a densely defined symmetric operator in a Hilbert…
A scaling hypothesis for the n-particle spectral densities of the O(3) nonlinear sigma-model is described. It states that for large particle numbers the n-particle spectral densities are ``self-similar'' in being basically rescaled copies…
Asymptotic couplings by reflection are constructed for a class of non-linear monotone SPDES (stochastic partial differential equations). As applications, the gradient/H\"older estimates as well as the exponential convergence are derived for…
We compute the spectral correlation functions for the transition from a harmonic oscillator towards the Gaussian Unitary Ensemble (GUE). We use a variant of the supersymmetry method to obtain analytical results in a fast and elegant way. In…
We consider a two-point correlator in massless $\phi^3$ model within the ladder approximation . The spectral density of the correlator is known explicitly and does not contain any resonances. Meanwhile making use of the standard sum rules…
Supersymmetric non-linear sigma-models are described by a field dependent Kaehler metric determining the kinetic terms. In general it is not guaranteed that this metric is always invertible. Our aim is to investigate the symmetry structure…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term…
Correlation functions provide information on the properties of mesons in vacuum and of hot nuclear matter. In this Letter, we present a new method to derive a well-defined spectral representation for correlation functions. Combining this…
We study the joint spectral properties of two coupled random matrices $H^{(1)}$ and $H^{(2)}$, which are either real symmetric or complex Hermitian. The entries of these matrices exhibit polynomially decaying correlations, both within each…
Speckle based imaging consists of forming a super-resolved reconstruction of an unknown sample from low-resolution images obtained under random inhomogeneous illuminations (speckles). In a blind context where the illuminations are unknown,…
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…
Network renormalization has traditionally relied on spatial adjacency-grouping nearby nodes together, but this approach fails to capture the dynamical correlations that govern system-wide behavior in scale-free networks. We present a…
A new recursion formula is presented for the correlation functions of the integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators involving n consecutive lattice sites to those with n-1 and n-2 sites. In a series of…