Related papers: Approximation to uniform distribution in SO(3)
The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator…
We project the Wilson/Polchinski renormalization group equation onto its uniform external field dependent effective free energy and connected Green's functions. The result is a hierarchy of equations which admits a choice of "natural"…
We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's…
We compute the generating function of random planar quadrangulations with three marked vertices at prescribed pairwise distances. In the scaling limit of large quadrangulations, this discrete three-point function converges to a simple…
In this paper we continue our program of extending the methods of geometric scattering theory to encompass the analysis of the Laplacian on symmetric spaces of rank greater than one and their geometric perturbations. In our previous work we…
Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point…
In physical systems possessing symmetry, reconstructing the underlying causal structure from observational data constitutes an inverse problem of fundamental importance. In this work, we formulate the inverse problem of causal inference…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
We evaluate partition functions of matrix models which are given by topologically twisted and dimensionally reduced actions of d=4 N=1 super Yang-Mills theories with classical (semi-)simple gauge groups, SO(2N), SO(2N+1) and USp(2N). The…
We develop a range-separated stochastic resolution of identity approach for the $4$-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic resolution of identity and the…
Many datasets in scientific and engineering applications are comprised of objects which have specific geometric structure. A common example is data which inhabits a representation of the group SO$(3)$ of 3D rotations: scalars, vectors,…
We show how rational function approximations to the logarithm, such as $\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$, can be turned into fast algorithms for approximating the determinant of a very large matrix. We empirically demonstrate that…
We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
The self-energy of the critical 3-dimensional O(N) model is calculated. The analysis is performed in the context of the Non-Perturbative Renormalization Group, by exploiting an approximation which takes into account contributions of an…
In a previous work [Andrade \textit{et al.}, Phys. Rep. \textbf{647}, 1 (2016)], it was shown that the exact Green's function (GF) for an arbitrarily large (although finite) quantum graph is given as a sum over scattering paths, where local…
We study the regularity of the score function in score-based generative models and show that it naturally adapts to the smoothness of the data distribution. Under minimal assumptions, we establish Lipschitz estimates that directly support…
In the first part of this article we obtain an identity relating the radial spectrum of rotationally invariant geodesic balls and an isoperimetric quotient $\sum 1/\lambda_{i}^{\rm rad}=\int V(s)/S(s)ds$. We also obtain upper and lower…
This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…
Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to…