Related papers: Singularities in Speckled Speckle: Statistics
Speckle is maybe the most fundamental interference effect of light in disordered media, giving rise to fascinating physical phenomena and enabling applications in imaging, spectroscopy or cryptography, to name a few. While speckle formed…
We study the intensity spatial correlation function of optical speckle patterns above a disordered dielectric medium in the multiple scattering regime. The intensity distributions are recorded by scanning near-field optical microscopy…
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.…
A brief overview of the current state of the problem of electromagnetic field singularities arising from the refraction and scattering of light by material objects is given. The discussion begins with caustics arising from ray tracing in…
The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period…
Intensity minima and maxima of speckle patterns obtained behind a diffuser are experimentally interchanged by applying a spiral phase delay of charge $\pm 1$ to the impinging coherent beam. This transform arises from the intuitive…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
A short resume is given about the nature of exceptional points (EPs) followed by discussions about their ubiquitous occurrence in a great variety of physical problems. EPs feature in classical as well as in quantum mechanical problems. They…
The two-point correlation function has been the standard statistic for quantifying how galaxies are clustered. The statistic uses the positions of galaxies, but not their properties. Clustering as a function of galaxy property, be it type,…
We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the…
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small…
The previously unknown property of the optical speckle pattern reported. The interference of a speckle with an oppositely moving phase-conjugated speckle wave produces a randomly distributed ensemble of a twisted entities (ropes)…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the…
In nonrelativistic quantum mechanics the spontaneous generation of singularities in smooth and finite wave functions, is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
We developed a dedicated statistical test for a massive detection of spot- and facula-crossing anomalies in multiple exoplanetary transit lightcurves, based on the frequentist $p$-value thresholding. This test was used to augment our…
Scattering can rapidly degrade our ability to form an optical image, to the point where only speckle-like patterns can be measured. Truly non-invasive imaging through a strongly scattering obstacle is difficult, and usually reliant on a…
We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances…
This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic…