Related papers: Weak convergence implies convergence in mean withi…
Weak convergence of the empirical copula process indexed by a class of functions is established. Two scenarios are considered in which either some smoothness of these functions or smoothness of the underlying copula function is required. A…
Rating prediction is a core problem in recommender systems to quantify user's preferences towards items, however, rating imbalance naturally roots in real-world user ratings that cause biased predictions and lead to poor performance on tail…
The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype…
The generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape…
Except for certain parameter values, a closed form formula for the mode of the generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from the literature on modified Bessel functions and their ratios to…
Let $\{X, X_n, n\geq 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \sum^n_{i=1} X_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n\ge 1.$ A weak convergence theorem is established for the…
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but…
The Weak Gravity Conjecture (WGC) was proposed to constrain Effective Field Theories (EFTs) with Abelian gauge symmetry coupled to gravity. In this article, I study the WGC from low energy observers' perspective, and revisit the issue of to…
The Cram\'er-Wold device characterises weak convergence of probability measures on $\mathbb{R}^d$ through convergence of all one-dimensional projected laws. We prove that, if the target projected laws are moment-determinate for…
We review various ways of obtaining consistency between the idea of supersymmetric grand unification and an apparent low value of $\alpha_s \sim 0.112$ indicated by several low energy experiments. We argue that to reconcile the low value of…
De Giorgi conjectured in 1979 that if a sequence of parabolic functionals Gamma converges to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. This paper studies the…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of…
We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of the domain serves as an outer obstacle, and the evolving…
We present an analysis of galaxy-galaxy weak gravitational lensing (GGL) in chameleon $f(R)$ gravity - a leading candidate of non-standard gravity models. For the analysis we have created mock galaxy catalogues based on dark matter haloes…
This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary foundation…
The promising solution to the strong CP problem by a Peccei-Quinn (PQ) symmetry may introduce quality and hierarchy problems, which are both relevant to Planck physics. In this paper, we study whether both problems can be explained by…
In this paper, we study the power of Gaussian curvature flow of a compact convex hypersurface and establish its Harnack inequality when the power is negative. In the Harnack inequality, we require that the absolute value of the power is…
We correlate the weak gravity conjecture (WGC), the KSS conjecture with chemical potential at extremality and the central charges by going through a particular example in five dimensional AdS spacetime with two unknown coefficients $c_1,…
We present Generalized Contrastive Divergence (GCD), a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithm for…