相关论文: Regular spectra in the vibron model with random in…

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…

In spite of its many successes, the Standard Model makes many empirical assumptions in the Higgs and fermion sectors for which a deeper theoretical basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2) \times su(3)$…

The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the…

Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher dimensional distributions to those targeting lower dimensional ones. This leads to a quasi-telescoping property of…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…

Electromagnetic interaction between a sub-wavelength particle (the `probe') and a material surface (the `sample') is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton…

We present here an explicit form of the random spectral measure element, what allows us to express a stationary random field as a stochastic integral explicitly depending on its power spectrum and a spectral tensor if the field is a vector…

We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…

The concept of unique normal form is formulated in terms of a spectral sequence. As an illustration of this technique some results of Baider and Churchill concerning the normal form of the anharmonic oscillator are reproduced. The aim of…

We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is…

A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…

We develop a statistical theory of the mean field. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction are random with the…

We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the…

The role of reflection symmetry breaking for the character of the appearance of replica symmetric spin glass state is investigated. We establish the following symmetry rule for classical systems with one order parameter in the replica…

We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…

Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. But typical mixtures interact through particular physical features, leading to a structured, non-random interaction…

We investigate interference of optical fields by examining the probability distribution of photon detection. The usual description of interference patterns in terms of superposition of classical mean fields with definite phases is…

We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…

We investigate the properties of sparse matrix ensembles with particular regard for the spectral ergodicity hypothesis, which claims the identity of ensemble and spectral averages of spectral correlators. An apparent violation of the…