Related papers: The Gaussian core model in high dimensions
We revisit Shannon's problem of bounding the capacity of bandlimited Gaussian channel (BLGC) with peak power constraint, and extend the problem to the peak-to-average-power-ratio (PAPR) constrained case. By lower bounding the achievable…
A Regge approach to the reaction processes $\gamma p\to\pi^-\Delta^{++}$ and $\gamma p\to\pi^+\Delta^0$ is presented for the description of existing data up to $E_\gamma= 16$ GeV. The model consists of the $t$-channel…
For a dilute system of non-relativistic bosons interacting through a positive $L^1$ potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1+…
We consider the stochastic heat equation driven by a multiplicative Gaussian noise that is white in time and spatially homogeneous in space. Assuming that the spatial correlation function is given by a Riesz kernel of order $\alpha \in…
We prove a sharp lower bound for the fundamental gap on convex domains in Gaussian spaces, the difference between the first two eigenvalues of the Ornstein-Uhlenbeck operator with Dirichlet boundary conditions. Our main result establishes…
In a 1979 paper, Ventevogel and Nijboer showed that classical point particles interacting via the pair potential $\phi(x)=\left(1+x^4\right)^{-1}$ are not equally spaced in their ground states in one dimension when the particle density is…
The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally…
We consider the possibility of a gravitationally induced particle production through the mechanism of a nonminimal curvature-matter coupling. An interesting feature of this gravitational theory is that the divergence of the energy-momentum…
Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…
The process e(+) e(-) -> n gamma (n>=2) are studied to estimate the total and differential cross sections of these reactions using the L3 data collected during 1991-1998 at centre of mass energies in the range 91-193 GeV. The lower limits…
We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…
We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition…
The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the…
Basing on recently developed convex programming framework in the paper [arXiv:2204.10626], we provide a proof for a long-standing conjecture on optimality of Gaussian encondings for the ultimate communication rate of generalized heterodyne…
It is well known that for a regular stable potential of pair interaction and a small value of activity one can define the corresponding Gibbs field (a measure on the space of configurations of points in $\mathbb{R}^d$). In this paper we…
Recent observations and theoretical considerations have motivated the study of models for dark energy with equation of state characterized by a parameter $w=p/\rho<-1$. Such models, however, are usually believed to be inviable due to their…
We derive a upper bound on the free energy of a Bose gas system at density $\rho$ and temperature $T$. In combination with the lower bound derived previously by Seiringer \cite{RS1}, our result proves that in the low density limit, i.e.,…
This is the first of two papers which study asymptotic behavior of minimal energy solutions to the fractional Lane-Emden system in a smooth bounded domain $\Omega$ \[(-\Delta)^s u = v^p, \quad (-\Delta)^s v = u^q \text{ in } \Omega \quad…
We prove that the complex Euclidean field theory with local quartic self-interaction in two dimensions arises as a limit of an interacting Bose gas at positive temperature, when the density of the gas becomes large and the range of the…
A confined quark model study in a couple of chirally anomalous processes is presented in comparison with effective meson Lagrangian approaches of various kind. The processes considered are \pi^0 \to \gamma \gamma and \gamma \to \pi^+ \pi^-…