Speaker: Hal Finkel
Title: Stochastic Evolution of Graphs using Local Moves
Abstract: Stochastic evolution of graphs is studied using rules taken from the dynamics of loop quantum gravity and spin-foam models. The results of using different combinations of generalized Pachner moves have been classified and qualitative constraints found which may be of interest for answering the question of when graphs are produced with emergent ``space-like'' characteristics. A number of different relevant properties, including statistical measures of dimension and the distribution of ``non-local'' edges, were found to be asymptotically stable. The results suggest that: 1. evolution based only on 1-to-3 moves of the kind generated by Thiemann's constraint yield spiky graphs with a statistical dimension close to one; 2. the addition of recoupling moves does lead to smoother and less spiking graphs; and 3. starting from a small random graph and evolving by generalized Pachner moves generally leads to large graphs with a significant number of non-local edges.
Talk: Transparencies, Recorded Talk