Related papers: Stein Type Characterization for $G$-normal Distrib…

Let G be a connected reductive group defined over a non-archimedean local field of characteristic 0. We assume G is quasi-split, adjoint and absolutly simple. Let g be the Lie algebra of G. We consider the space of the invariant…

Stein's method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we…

Let $D$ be a non-commutative division ring, $G$ a subnormal subgroup of ${\mathrm GL}_n(D)$. In this note we show that if $G$ contains a non-abelian solvable maximal subgroup, then $n=1$ and $D$ is a cyclic algebra of prime degree over $F$.

Here, we introduce a new definition of regular point for piecewise-linear (PL) functions on combinatorial (PL triangulated) manifolds. This definition is given in terms of the restriction of the function to the link of the point. We show…

Jamming occurs in granular materials, as well as in emulsions, dense suspensions, and other amorphous, particulate systems. When the packing fraction $\phi$, defined as the ratio of particle volume to system volume, is increased past a…

Let $X$ be a finite set such that $|X|=n$. Let $\trans$ and $\sym$ denote respectively the transformation monoid and the symmetric group on $n$ points. Given $a\in \trans\setminus \sym$, we say that a group $G\leq \sym$ is $a$-normalizing…

It is well known that the lattice Idc G of all principal {\ell}-ideals of any Abelian {\ell}-group G is a completely normal distributive 0-lattice, and that not every completely normal distributive 0-lattice is a homomorphic image of some…

We consider data from the Grassmann manifold $G(m,r)$ of all vector subspaces of dimension $r$ of $\mathbb{R}^m$, and focus on the Grassmannian statistical model which is of common use in signal processing and statistics. Canonical…

We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…

Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. However, biological gene-regulatory pathways are more complex than simple Turing activator-inhibitor…

In a recent paper, Gaunt 2020 extended Stein's method to limit distributions that can be represented as a function $g:\mathbb{R}^d\rightarrow\mathbb{R}$ of a centered multivariate normal random vector $\Sigma^{1/2}\mathbf{Z}$ with…

The Standard Model (SM) is a chiral theory, where right- and left-handed fermion fields transform differently under the gauge group. Extra fermions, if they do exist, need to be heavy otherwise they would have already been observed. With no…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

We study the global and the local transport and diffusion in the case of the standard map, by calculating the diffusion exponent $\mu$. In the global case we find that the mean diffusion exponent for the whole phase space is either $\mu=1$,…

High resolution (R$\sim$22,500) spectra for 400 red clump giants, in four fields within $\rm -4.8^{\circ} \lesssim b \lesssim -3.4^{\circ}$ and $\rm -10^{\circ} \lesssim l \lesssim +10^{\circ}$, were obtained within the GIRAFFE Inner Bulge…

We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined…

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…

With an aim to shed light on the origin of Li anomaly observed in a small fraction of red giants, we carried out a spectroscopic study on the observational characteristics of selected 20 bright Li-rich giants, in comparison with a large…

We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion $$ \partial_tu+(-\Delta)^{\sigma/2}\varphi(u)=0, $$ posed for $x\in \mathbb{R}^N$, $t>0$, with $0<\sigma<2$, $N\ge1$. If the…

Let $\mathcal{T}$ be the set of spanning trees of $G$ and let $L(T)$ be the number of leaves in a tree $T$. The leaf number $L(G)$ of $G$ is defined as $L(G)=\max\{L(T)|T\in \mathcal{T}\}$. Let $G$ be a connected graph of order $n$ and…