Related papers: The Gaussian core model in high dimensions
Through refined asymptotic analysis based on the normal approximation, we study how higher-order coding performance depends on the mean power as well as on finer statistics of the input power. We introduce a multifaceted power model in…
We study the lowest energy E of a semirelativistic system of N identical massless bosons with Hamiltonian H= sum{i=1 to N} sqrt(p_i^2)+ sum{j>i=1 to N} g |r_i - r_j|^2, g > 0. We prove the inequalities A [g N^2 (N-1)^2]^{1/3} < E < B [g N^2…
In these lectures we present a brief review of the Higgs boson sector in the ``Standard Model'', and its Minimal Supersymmetric Extension, with particular emphasis on the main mechanisms for Higgs production and decay at LEP2 and LHC, and…
The strength of quantum correlations is bounded from above by Tsirelson's bound. We establish a connection between this bound and the fact that correlations between two systems cannot increase under local operations, a property known as the…
We explore the performance of a statistical learning technique based on Gaussian Process (GP) regression as an efficient non-parametric method for constructing multi-dimensional potential energy surfaces (PES) for polyatomic molecules.…
The development of computational resources has made it possible to determine upper bounds for atomic and molecular energies with high precision. Yet, error bounds to the computed energies have been available only as estimates. In this…
We consider the precision $\Delta \varphi$ with which the parameter $\varphi$, appearing in the unitary map $U_\varphi = e^{ i \varphi \Lambda}$ acting on some type of probe system, can be estimated when there is a finite amount of prior…
The computation of the polarized amplitudes and cross section of the processes $\gamma\nu\to\gamma\gamma \nu$, $\gamma\gamma \to \gamma\nu\bar\nu$ and $\nu\bar\nu \to \gamma\gamma\gamma$ is described. We used an effective lagrangian…
Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…
In this paper, we introduce a novel bond-based peridynamic model that utilizes a Gaussian kernel function. Previous peridynamic models, when directly discretized, have exhibited a lack of asymptotically compatibility with their…
We derive upper bounds for the potential energy of spherical designs of cardinality close to the Delsarte-Goethals-Seidel bound. These bounds are obtained by linear programming with the use of the Hermite interpolating polynomial of the…
We prove that the gravitational binding energy {\Omega} of a self gravitating system described by a mass density distribution {\rho}(x) admits an upper bound B[{\rho}(x)] given by a simple function of an appropriate, non-additive Tsallis'…
We show that correlation functions have to satisfy contraint relations, owing to the non-negativity of the power spectrum of the underlying random process. Specifically, for any statistically homogeneous and (for more than one spatial…
We study isometric immersions of a Riemannian surface $(\Omega,\frak{g})$, where $\Omega \subset \mathbb{R}^2$, into $\mathbb{R}^3$. We consider their bending energy, i.e., the square of the $L^2$-norm of their second fundamental form,…
We consider a system of $d$ non-linear stochastic fractional heat equations in spatial dimension $1$ driven by multiplicative $d$-dimensional space-time white noise. We establish a sharp Gaussian-type upper bound on the two-point…
We study the lowest energy E of a relativistic system of N identical bosons bound by harmonic-oscillator pair potentials in three spatial dimensions. In natural units the system has the semirelativistic ``spinless-Salpeter'' Hamiltonian H =…
In quantum theory it is generally assumed that there exists a special state called the vacuum state and that this state is a lower bound to the energy. However it has recently been demonstrated that this is not necessarily the case for some…
We present a method to extract the low energy behavior of physical observables from their high energy expansions, systematically calculable via the operator product expansion (OPE), in asymptotically free and mass-gapped theories. By…
We give a simple proof of a lower bound for the Dirichlet heat kernel in terms of the Gaussian heat kernel. Using this we establish a non-existence result for semilinear heat equations with zero Dirichlet boundary conditions and initial…
We discuss the physics of the 3+1 dimensional lambda Phi^4 quantum field theory in terms of the statistical mechanics of a gas of particles (`atoms') that interact via a -1/r^3-plus-hard-core potential. The hard-core potential,…