Related papers: Inference of Boundaries in Causal Sets

The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect…

Matter density is formally infinite at the location of caustic surfaces, where dark matter sheet folds in phase-space. The caustics separate regions with different number of streams and the volume elements change the parity by turning…

This paper studies regularity of perimiter quasiminimizing sets in metric measure spaces with a doubling measure and a Poincare inequality. The main result shows that the measure theoretic boundary of a quasiminimizing set coincides with…

A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and…

We propose a 2+1d simulation of Energetic Causal Sets (ECS). These are a class of Causal Sets where the agency of time and its irreversibility are taken as fundamental. Events are endowed with energy-momentum conservation laws being applied…

A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…

The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…

The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of…

This paper investigates instances of Sobolev embeddings characterized by local compactness at every point within their domain, except for a single point. We obtain the sharp conditions that distinguish compactness from non-compactness and…

Overlap between treatment groups is required for non-parametric estimation of causal effects. If a subgroup of subjects always receives the same intervention, we cannot estimate the effect of intervention changes on that subgroup without…

The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…

We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle…

This article is concerned with causal structures, which are defined as a field of tangentially non-degenerate projective hypersurfaces in the projectivized tangent bundle of a manifold. The local equivalence problem of causal structures on…

The causal boundary construction of Geroch, Kronheimer, and Penrose has some universal properties of importance for general studies of spacetimes, particularly when equipped with a topology derived from the causal structure. Properties of…

We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary in $d$-dimensional Minkowski spacetime. When the boundary is a single plane we compute the…

We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first…

We propose, for dimension d, a discrete Lorentz invariant operator on scalar fields that approximates the Minkowski spacetime scalar d'Alembertian. For each dimension, this gives rise to a scalar curvature estimator for causal sets, and…

We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The…

We propose a measure of holographic information based on a causal wedge construction. The motivation behind this comes from an attempt to understand how boundary field theories can holographically reconstruct spacetime. We argue that given…