From trees to gravity
Chapter in Handbook of Quantum Gravity, Spinger (2023)
Abstract:
In this article, we study two related models of quantum geometry: generic random trees and two-dimensional causal triangulations. The Hausdorff and spectral dimensions that arise in these models are calculated, and their relationship with the structure of the underlying random geometry is explored. Modifications due to interactions with matter fields are also briefly discussed. The approach to the subject is that of classical statistical mechanics, and most of the tools come from probability and graph theory.From Trees to Gravity
(2022)
The Size of a Soliton
(2022)
The cylinder amplitude in the hard dimer model on 2D Causal Dynamical Triangulations
Classical and Quantum Gravity IOP Publishing 39:7 (2022) 075004
Abstract:
We consider the model of hard dimers coupled to two-dimensional causal dynamical triangulations (CDT) with all dimer types present and solve it exactly subject to a single restriction. Depending on the dimer weights there are, in addition to the usual gravity phase of CDT, two tri-critical and two dense dimer phases. We establish the properties of these phases, computing their cylinder and disk amplitudes, and their scaling limits.The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations
(2021)