Related papers: Mean density of inhomogeneous Boolean models with …
The trace anomaly of dense matter, $\Delta \equiv 1/3 - P/\varepsilon$, defined through the ratio $w \equiv P/\varepsilon$ of pressure $P$ to energy density $\varepsilon$, quantifies deviations from conformal symmetry and provides a…
We investigate the inference of varifold structures in a statistical framework: assuming that we have access to i.i.d. samples in $\mathbb{R}^n$ obtained from an underlying $d$--dimensional shape $S$ endowed with a possibly non uniform…
New developments have been brought to our energy-, spin- and parity-dependent nuclear level densities based on the microscopic combinatorial method. Our new calculation is based on the BSkG3 mean-field model which relies on a…
We explicitly calculate Janossy densities for a special class of finite determinantal point processes with several types of particles introduced by Pr\"ahofer and Spohn and, in the full generality, by Johansson in connection with the…
We prove that if $E \subseteq \mathbb{R}^d$ ($d\geq 2$) is a Lebesgue-measurable set with density larger than $\frac{n-2}{n-1}$, then $E$ contains similar copies of every $n$-point set $P$ at all sufficiently large scales. Moreover,…
In Weil (2001) formulas were proved for stationary Boolean models $Z$ in $\mathbb{R}^d$ with convex or polyconvex grains, which express the densities of mixed volumes of $Z$ in terms of related mean values of the underlying Poisson particle…
The long-range spectral density correlations (spectral rigidities $\bar{\Delta}_3(\bar n)$ and related spectral compressibilities) of the $E\otimes (b_1+b_2)$ Jahn-Teller model are found strongly nonuniversal with respect to the Hamiltonian…
We study the problem of the nonparametric estimation for the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$. From the continuous observation of the sampling path on…
This paper deals with studying vague convergence of random measures of the form $\mu_{n}=\sum_{i=1}^{n} p_{i,n} \delta_{\theta_i}$, where $(\theta_i)_{1\le i \le n}$ is a sequence of independent and identically distributed random variables…
The Hubble tension casts a blight on the standard cosmology. As a possible solution to the problem, the local variation of the expansion rate has been proposed where the spatial averaging over a finite domain was introduced in order to…
The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert-Schmidt and Bures-Hall ensembles. In this…
The $\beta$-Delaunay tessellation in $\mathbb{R}^{d-1}$ is a generalization of the classical Poisson-Delaunay tessellation. As a first result of this paper we show that the shape of a weighted typical cell of a $\beta$-Delaunay…
Recently, Bollob\'as, Janson and Riordan introduced a very general family of random graph models, producing inhomogeneous random graphs with $\Theta(n)$ edges. Roughly speaking, there is one model for each {\em kernel}, i.e., each symmetric…
Metric mean dimension is a geometric invariant of dynamical systems with infinite topological entropy. We relate this concept with the fractal structure of the phase space and the H\"older regularity of the map. Afterwards we improve our…
The density functional renormalization group (density-fRG) is proposed to investigate the density fluctuations within the functional renormalization group approach, which allows us to quantify the medium effect and study physics of high…
For an arbitrary Radon measure $\mu$ we estimate the integrated discrete curvature of $\mu$ in terms of its centred variant of Jones' beta numbers. We farther relate integrals of centred and non-centred beta numbers. As a corollary,…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found…
We study the distributions of the random Dirichlet series with parameters $(s, \beta)$ defined by $$ S=\sum_{n=1}^{\infty}\frac{I_n}{n^s}, $$ where $(I_n)$ is a sequence of independent Bernoulli random variables, $I_n$ taking value $1$ with…
One of the basic aims of this paper is to study the relationship between the geometry of ``hypersurface like'' subsets of Euclidean space and the properties of the measures they support. In this context we show that certain doubling…