Related papers: Path length distribution in two-dimensional causal…

This paper studies the distribution of chain and maximal chain lengths in a causal set. We first provide a new derivation for these distributions for a causal set uniformly embedded in Minkowski space, for various dimensionalities, which…

We describe numerical and analytical investigations of causal sets sprinkled into spacetime manifolds. The first part of the paper is a numerical study of finite causal sets sprinkled into Alexandrov subsets of Minkowski spacetime of…

Aleksandrov, and then Zeeman, showed that the causal relations among the set of points in a Minkowski space of dimension greater than 2 determine the Minkowski space structure of the set up to a global conformal factor. We show that in any…

We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…

This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains…

We investigate the extrinsic geometry of causal sets in $(1+1)$-dimensional Minkowski spacetime. The properties of boundaries in an embedding space can be used not only to measure observables, but also to supplement the discrete action in…

We present a new method for embedding a causal set into Minkowski spacetime. The method is similar to a previously presented method, but is simpler and provides better embedding results. The method uses spacetime volumes to define causal…

We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to…

The causal set action of dimension $d$ is investigated for causal sets that are Poisson sprinklings into submanifolds of $d$-dimensional Minkowski space. Evidence, both analytic and numerical, is provided for the conjecture that the mean of…

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…

Citation networks represent the flow of information between agents. They are constrained in time and so form directed acyclic graphs which have a causal structure. Here we provide novel quantitative methods to characterise that structure by…

Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…

Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly…

A criticism sometimes made of the causal set quantum gravity program is that there is no practical scheme for identifying manifoldlike causal sets and finding embeddings of them into manifolds. A computational method for constructing an…

A list of all possible causal relations in the $2$-dimensional Minkowski space $M$ is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating…

We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for {\it (i)} the effect of the finite size of the system, and {\it (ii)} the dependence…

The structure of $k$-diametral point configurations in Minkowski $d$-space is shown to be closely related to the properties of $k$-antipodal point configurations in $\mathbb{R}^d$. In particular, the maximum size of $k$-diametral point…

Randomly sampling an acyclic orientation on the complete bipartite graph $K_{n,k}$ with parts of size $n$ and $k$, we investigate the length of the longest path. We provide a probability generating function for the distribution of the…

In order to understand the detailed mechanism by which a fundamental discreteness can provide a finite entanglement entropy, we consider the entanglement entropy of two classes of free massless scalar fields on causal sets that are well…

We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short…