27 citations · 65 across the 6 of their papers we have counts for
6 papers
Oliver Curvature Bounds for the Brownian Continuum Random Tree
Christy Kelly
We compute bounds in the expected Ollivier curvature for the Brownian continuum random tree . The results indicate that when the scale dependence of the O…
Convergence of Combinatorial Gravity
Christy Kelly, Carlo Trugenberger, Fabio Biancalana
We present a new regularisation of Euclidean Einstein gravity in terms of (sequences of) graphs. In particular, we define a discrete Einstein-Hilbert action that converges to its m…
Emergence of the Circle in a Statistical Model of Random Cubic Graphs
Christy Kelly, Carlo Trugenberger, Fabio Biancalana
We consider a formal discretisation of Euclidean quantum gravity defined by a statistical model of random -regular graphs and making using of the Ollivier curvature, a coarse an…
Exact Expressions and Reduced Linear Programmes for the Ollivier Curvature in Graphs
Christy Kelly
The Ollivier curvature has important applications in discrete geometry and network theory, in particular as a measure of local clustering. The Ollivier curvature is defined in term…
Self-Assembly of Geometric Space from Random Graphs
Christy Kelly, Carlo A Trugenberger, Fabio Biancalana
We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven…
Combinatorial Quantum Gravity: Emergence of Geometric Space from Random Graphs
C. Kelly, C. A. Trugenberger
We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is…