Related papers: A Mathematical Theory of Stochastic Microlensing I…
Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…
The unprecedented amount and the excellent quality of lensing data that the upcoming ground- and space-based surveys will produce represent a great opportunity to shed light on the questions that still remain unanswered concerning our…
In recent years, gravitational lensing has been used as a means to detect substructure in galaxy-sized halos, via anomalous flux ratios in quadruply-imaged lenses. In addition to causing anomalous flux ratios, substructure may also perturb…
We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
The last few years have seen the development of a promising theoretical framework for statistics of the cosmic large-scale structure -- the theory of large deviations (LDT) for modelling weak-lensing one-point statistics in the mildly…
It is conventional to calculate the probability of microlensing for a cosmologically distant source based on the Press-Gunn approximation that the lensing objects are uniformly and randomly distributed in the intervening space with a…
We study the local behavior of gravitational lensing near fold catastrophes. Using a generic form for the lensing map near a fold, we determine the observable properties of the lensed images, focusing on the case when the individual images…
Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant…
The weak-lensing science of the LSST project drives the need to carefully model and separate the instrumental artifacts from the intrinsic lensing signal. The dominant source of the systematics for all ground based telescopes is the spatial…
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…
Weak lensing of galaxies and CMB photons through the large-scale structure of the Universe is one of the most promising cosmological probes with upcoming experiments dedicated to its measurements such as Euclid/LSST and CMB Stage 4…
The central ambition of the modern time delay cosmography consists in determining the Hubble constant $H_0$ with a competitive precision. However, the tension with $H_0$ obtained from the Planck satellite for a spatially-flat $\Lambda$CDM…
Anisotropy in the point spread function (PSF) contributes a systematic error to weak lensing measurements. In this study we use a ray tracer that incorporates all the optical elements of the SNAP telescope to estimate this effect.…
The time delay between the arrival of photons of multiple images of time variable sources can be used to constrain absolute distances in the Universe (Refsdal 1964), and in turn obtain a direct estimate of the Hubble constant and other…
We describe an efficient algorithm for calculating the statistics of weak lensing by large-scale structure based on a tiled set of independent particle-mesh N-body simulations which telescope in resolution along the line of sight. This…
Statistics of the weak lensing of galaxies can be used to constrain cosmology if the galaxy shear can be estimated accurately. In general this requires accurate modelling of unlensed galaxy shapes and the point spread function (PSF). I…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
Point spread function (PSF) plays an essential role in image reconstruction. In the context of confocal microscopy, optical performance degrades towards the edge of the field of view as astigmatism, coma and vignetting. Thus, one should…