Related papers: Approximation to uniform distribution in SO(3)
We study expected Riesz s-energies and linear statistics of some determinantal processes on the sphere. In particular, we compute the expected Riesz and logarithmic energies of the determinantal processes given by the reproducing kernel of…
We describe several randomized collections of $3\times 3$ rotation matrices and analyze their associated logarithmic energy. The best one (i.e. the one attaining the lowest expected logarithmic energy) is constructed by choosing $r$…
We show the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of $k$ independent $n\times n$ matrices with i.i.d. complex Gaussian entries with a few…
We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to…
We study estimates of the Green's function in $\mathbb{R}^d$ with $d \ge 2$, for the linear second order elliptic equation in divergence form with variable uniformly elliptic coefficients. In the case $d \ge 3$, we obtain estimates on the…
Estimating the 3DoF rotation from a single RGB image is an important yet challenging problem. Probabilistic rotation regression has raised more and more attention with the benefit of expressing uncertainty information along with the…
We calculate the Green's functions for the particle-vortex system, for two anyons on a plane with and without a harmonic regulator and in a uniform magnetic field. These Green's functions which describe scattering or bound states (depending…
Estimating the 3DoF rotation from a single RGB image is an important yet challenging problem. As a popular approach, probabilistic rotation modeling additionally carries prediction uncertainty information, compared to single-prediction…
In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a…
In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper…
In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a…
We compute the expected Riesz energy of random points on flat tori drawn from certain translation invariant determinantal processes and determine the process in the family providing the optimal asymptotic expected Riesz energy.
It is shown that general dilepton angular distribution (with parity violating terms taking into account) in vector particle decays can be described through a set of five SO(3) rotational-invariant observables. These observables are derived…
We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence…
We define a determinantal point process on the complex projective space that reduces to the so-called spherical ensemble for complex dimension 1 under identification of the 2-sphere with the Riemann sphere. Through this determinantal point…
We introduce a technique to obtain pointwise upper and lower bounds for the Green's function of elliptic operators whose principal part is the Laplacian and that include a drift term diverging near the boundary like a power of the inverse…
We prove a generalized version of the $3G$ Principle for Green's functions on bounded inner uniform domains in a wide class of Dirichlet spaces. In particular, our results apply to higher-dimensional fractals such as Sierpinski carpets in…
We study the Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$ of $2$-dimensional subspaces of $\mathbb{R}^4$. We prove that the continuous Riesz and logarithmic energies are uniquely minimized by the uniform…
Determinantal point processes exhibit an inherent repulsive behavior, thus providing examples of very evenly distributed point sets on manifolds. In this paper, we study the so-called harmonic ensemble, defined in terms of Laplace…
Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particle as a…