Related papers: Planar Projections and Second Intrinsic Volume
We study random convex cones defned as positive hulls of $d$-dimensional random walks and bridges. We compute expectations of various geometric functionals of these cones such as the number of $k$-dimensional faces and the sums of conic…
We prove a conjecture of Aanjaneya, Bishnu, and Pal that the minimum number of diffuse reflections sufficient to illuminate the interior of any simple polygon with $n$ walls from any interior point light source is $\lfloor n/2 \rfloor - 1$.…
We explore perturbative double field theory about time-dependent (cosmological) backgrounds to cubic order. To this order the theory is consistent in a weakly constrained sense, so that for a toroidal geometry it encodes both momentum and…
For volume reflection process in a bent crystal, exact analytic expressions for positively- and negatively-charged particle trajectories are obtained within a model of parabolic continuous potential in each interplanar interval, with the…
The intrinsic alignment of galaxies with the large-scale density field is an important astrophysical contaminant in upcoming weak lensing surveys. We present detailed measurements of the galaxy intrinsic alignments and associated…
We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs.…
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…
The properties of universes are explored that are entirely in the interior of black holes in another universe, a `mother universe'. It is argued that these models offer a paradigm that may shed a new light on old cosmological problems. The…
We present a study of cubic surfaces from the novel perspective of positive geometry. Our positive geometries have dimension two (the surface minus its 27 lines), dimension three (its complement in 3-space), and dimension four (the moduli…
Let T be a random triangle in a disk D of radius R (meaning that vertices are independent and uniform in D). We determine the bivariate density for two arbitrary sides a,b of T. In particular, we compute that E(a*b)=(0.837...)*R^2, which…
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the…
In this paper we will consider an unknown binary image, of which the length of the boundary and the area of the image are given. These two values together contain some information about the general shape of the image. We will study two…
For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely its sectional curvature and scalar curvature on one side;…
We discuss a few examples in 2+1 dimensions and 1+1 dimensions supporting a recent conjecture concerning the relation between the Planck scale and the coupling strength of a non-gravitional interaction, unlike those examples in 3+1…
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
Quantum aspects of black holes may have observational imprints on their absorption and emission spectrum. In this work, we consider the possibility of non-uniform area quantization and its effects on the phasing of gravitational waveform…
Many modern applications of Bayesian inference, such as in cosmology, are based on complicated forward models with high-dimensional parameter spaces. This considerably limits the sampling of posterior distributions conditioned on observed…
Correlations between the magnification or polarization of background sources, induced by gravitational lensing due to the large-scale structure, and the positions of foreground galaxies are investigated. We found that their amplitude is…
We present a semi-analytic model for the shear two-point correlation function of a cosmic shear survey with non-uniform depth. Ground-based surveys are subject to depth variations that primarily arise through varying atmospheric conditions.…
Generalising the two-dimensional case, we provide estimates for the mean-values of the lengths of the edges of an integral box with given volume and minimal surface.