Related papers: A Mathematical Theory of Stochastic Microlensing I…
The first half of this paper explores the origin of systematic biases in the measurement of weak gravitational lensing. Compared to previous work, we expand the investigation of PSF instability and fold in for the first time the effects of…
The analysis of optical images of galaxy-galaxy strong gravitational lensing systems can provide important information about the distribution of dark matter at small scales. However, the modeling and statistical analysis of these images is…
The standard weak lensing formalism assumes that the lensing map relating the observed image of a source to its intrinsic shape depends only on the deflection angle. We show that this description is incomplete beyond linear perturbation…
Gravitational microlensing is currently the only technique that helps study the Galactic distribution of planets as a function of distance from the Galactic center. The Galactic location of a lens system can be uniquely determined only when…
Distribution of galaxies may be a biased tracer of the dark matter distribution and the relation between the galaxies and the total mass may be stochastic, non-linear and time-dependent. Since many observations of galaxy clustering will be…
While time-delay lenses can be an independent probe of $H_0$ the estimates are degenerate with the convergence of the lens near the Einstein radius. Velocity dispersions, $\sigma$, can be used to break the degeneracy, with uncertainties…
We present a method for computing the probability distribution of microlensed light curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper…
The LSST survey will provide unprecedented statistical power for measurements of dark energy. Consequently, controlling systematic uncertainties is becoming more important than ever. The LSST observing strategy will affect the statistical…
We reanalyzed spectra that were taken as part of the SL2S lens galaxy survey with the goal to obtain the stellar velocity dispersion with a precision and accuracy sufficient for time-delay cosmography. In order to achieve this goal, we…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
We study the weak gravitational lensing effects caused by a stochastic distribution of dark matter halos. We develop a simple approach to calculate the magnification probability distribution function which allows us to easily compute the…
We compute a microlensing map for the Galactic bar. The predicted event rate and event duration distribution are consistent with the $55$ events recently reported by the MACHO and OGLE collaborations. Most of the events are due to lensing…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
It is believed that the biasing of the galaxies plays an important role for understanding the large-scale structure of the universe. In general, the biasing of galaxy formation could be stochastic. Furthermore, the future galaxy survey…
We estimate the rate of near-field microlensing events expected from all-sky surveys and investigate the properties of these events. Under the assumption that all lenses are composed of stars, our estimation of the event rate ranges from…
Weak lensing by large-scale structure is an invaluable cosmological tool given that most of the energy density of the concordance cosmology is invisible. Several large ground-based imaging surveys will attempt to measure this effect over…
Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
The gravitational field of a galaxy can act as a lens and deflect the light emitted by a more distant object such as a quasar. Strong gravitational lensing causes multiple images of the same quasar to appear in the sky. Since the light in…