Related papers: The Shape of the Noncentral Chi-square Density

This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities. We demonstrate that Least Squares EM, a variant of the EM algorithm, converges to the true location parameter from a randomly…

Let $f$ be a Hecke--Maass cuspidal newform of square-free level $N$ and Laplacian eigenvalue $\lambda$. It is shown that $\pnorm{f}_\infty \ll_{\lambda,\epsilon} N^{-1/6}+\epsilon} \pnorm{f}_2$ for any $\epsilon>0$.

In the class of nonlinear one-parameter real maps we study those with bifurcation that exhibits period doubling cascade. The fixed points of such a map form a finite discrete real set with dimension (2^n)m, where m is the (odd) number of…

We define a measure of noncompactness $\lambda$ on the standard Hilbert $C^*$-module $l^2(\mathcal A)$ over a unital $C^*$-algebra, such that $\lambda(E)=0$ if and only if $E$ is $\mathcal A$-precompact (i.e.\ it is $\varepsilon$-close to a…

We consider distributional limit of the Pearson chi-square statistic when the number of classes m increases with the sample size n in such way that $n/\sqrt{m} \to {\lambda}$. Under mild moment conditions, the limit is Gaussian for…

We have investigated a weighted chi-square distribution of the variable $\xi$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $\phi_k=2\pi k/N$, where $k \in \{0,1,...,N-1\}$…

We prove that any $n$-dimensional closed mean convex $\lambda$-hypersurface is convex if $\lambda\le 0.$ This generalizes Guang's work on $2$-dimensional strictly mean convex $\lambda$-hypersurfaces. As a corollary, we obtain a gap theorem…

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory…

We study the isoperimetric problem on $\mathbb{R}^1$ with a prescribed density function $f$ that affects how area and perimeter are measured. We examine density functions that are symmetric, radially increasing, and satisfy two additional…

Let f be an $L^2$-normalized weight zero Hecke-Maass cusp form of square-free level N, character $\chi$ and Laplacian eigenvalue $\lambda\geq 1/4$. It is shown that $\| f \|_{\infty} \ll_{\lambda} N^{-1/37}$, from which the hybrid bound…

Non-compact three-dimensional QED is studied by computer simulations to understand its chiral symmetry breaking features for N_f>=2, on lattice volumes up to 50^3 and bare masses as low as ma=0.0000625. We compute the chiral condensate,…

We study level number variance in a two-dimensional random matrix model characterized by a power-law decay of the matrix elements. The amplitude of the decay is controlled by the parameter b. We find analytically that at small values of b…

In general the kernel of QCD's gap equation possesses a domain of analyticity upon which the equation's solution at nonzero chemical potential is simply obtained from the in-vacuum result through analytic continuation. On this domain the…

By the Pr\'ekopa-Leindler inequality, the difference $X-X'$ has a log-concave density provided that $X$ has a log-concave density and $X, X'$ are independent and identically distributed. We prove that the opposite direction does not always…

We use density--functional theory to study the structure of two-dimensional defects inside a circular nematic nanocavity. The density, nematic order parameter, and director fields, as well as the defect core energy and core radius, are…

We investigate the statistics of stationary points in the sum of squares of $N$ Gaussian random fields, which we call a "chi-squared" field. The behavior of such a field at a point is investigated, with particular attention paid to the…

Overlap fermions, which preserve exact chiral symmetry on the lattice, provide a powerful tool for investigating the topological structure of the vacuum. Applying this formulation to zero-temperature quenched SU(3) configurations generated…

The estimation of a log-concave density on $\mathbb{R}$ is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet…

We analyse the $\Gamma$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk…

Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…