相关论文: On the relationship between mean observations, spa…
We study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in [Hairer, Weber, Probab. Theory…
Improvement of the prediction accuracy of the Earth's rotation parameters (ERP) is one of the main problems of applied astrometry. In order to solve this problem, various approaches are used and in order to select the best one, comparison…
The relation between angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. This model has large inhomogeneities of matter distribution on small scales. We have discovered that the relation agrees…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
We establish effective convergence rates in the Doeblin-Lenstra law, describing the limiting distribution of approximation coefficients arising from continued fraction convergents of a typical real number. More generally, we prove…
The redshift drift (also known as the Sandage Test) is a model-independent probe of fundamental cosmology, enabling us to watch the universe expand in real time, and thereby to confirm (or not) the recent acceleration of the universe…
High redshift sources suffer from magnification or demagnification due to weak gravitational lensing by large scale structure. One consequence of this is that the distance-redshift relation, in wide use for cosmological tests, suffers…
This paper is motivated by the problem of quantitatively bounding the convergence of adaptive control methods for stochastic systems to a stationary distribution. Such bounds are useful for analyzing statistics of trajectories and…
We derive quantitative bounds on the rate of convergence in $L^1$ Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the…
We study the form of the luminosity distance as a function of redshift in the presence of large scale inhomogeneities, with sizes of order 10 Mpc or larger. We approximate the Universe through the Swiss-cheese model, with each spherical…
We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of…
We assess the dominant low-redshift anisotropic signatures in the distance-redshift relation and redshift drift signals. We adopt general-relativistic irrotational dust models allowing for gravitational radiation -- the `quiet universe…
The next generation of telescopes will usher in an era of precision cosmology, capable of determining the cosmological model to beyond the percent level. For this to be effective, the theoretical model must be understood to at least the…
Much of the science that is made possible by multiwavelength redshift surveys requires the use of photometric redshifts. But as these surveys become more ambitious, and as we seek to perform increasingly accurate measurements, it becomes…
High precision astrometry now enables to measure the time drift of astrophysical observables in real time, hence providing new ways to probe different cosmological models. This article presents a general derivation of the redshift and…
The Einstein Telescope and other third generation interferometric detectors of gravitational waves are projected to be operational post $2030$. The cosmological signatures of gravitational waves would undoubtedly shed light on any departure…
A new formalism in general relativity with a linear response relation between perturbed Einstein tensor and the stress-energy tensor is presented. Basic concepts are borrowed from statistical physics and theory of stochastic processes by…
We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on ${\mathbb R}^d$. In this setting, the objective is in general not…
Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…
Distance-redshift data can impose strong constraints on dark energy models even when the equation of state is oscillatory. Despite the double integral dependence of the distance on the equation of state, precision measurement of the…