相关论文: Extreme Geometric Quantiles Under Minimal Assumpti…
We consider epimorphisms and several variant notions -- split, effective, regular, strong, and extremal -- and determine which of these coincide in the metric coarse and coarsely Lipschitz categories. In particular, we characterise extremal…
Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary…
Fractons and other subdimensional particles are an exotic class of emergent quasi-particle excitations with severely restricted mobility. A wide class of models featuring these quasi-particles have a natural description in the language of…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show…
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar…
We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…
We use the notion of generalized connection over a bundle map in order to present an alternative approach to sub-Riemannian geometry. Known concepts, such as normal and abnormal extremals, will be studied in terms of this new formalism. In…
We analyze the extremality and decomposability properties with respect to two types of nonlocal perimeters available in the literature, the Gagliardo perimeter based on the eponymous seminorms and the nonlocal distributional Caccioppoli…
The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile…
This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained…
Introducing the concept of the extreme trapping horizon, we discuss geometric features of dynamical extreme black holes in four dimensions and then derive the integral identities which hold for the dynamical extreme black holes. We address…
Canonical quantization of the polarized Gowdy midi-superspace with a 3-torus spatial topology is carried out. As in an earlier work on the Einstein-Rosen cylindrical waves, symmetry reduction is used to cast the original problem in…
We resolve a conjecture of Kalai relating approximation theory of convex bodies by simplicial polytopes to the face numbers and primitive Betti numbers of these polytopes and their toric varieties. The proof uses higher notions of…
We study weighted simultaneous rational approximation to points of the form $(1,\xi,\xi^2)$, for a class of extremal real numbers $\xi$, within the framework of multi-parametric geometry of numbers.
We propose a method for demonstrating equivalences beyond the saddlepoint approximation between quantities in quantum gravity that are defined by the Euclidean path integral, without assumptions about holographic duality. The method…
The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed,…
We consider stationary sequences whose marginal tail is subexponential and lies in the Gumbel Maximum domain of attraction. Due to the extremely strong dependence, their extreme values are caused by multiple big values and are clustered in…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses…