Next steps in understanding the asymptotics of $3d$ quantum gravity
Based on a combinatorial approach and random matrix theory, we show a central limit theorem that gives important insight into causally triangulated $3d$ quantum gravity.
math-ph↗
arXiv subjects
Maria Simonetta Bernabei
Publications and source records attributed to Maria Simonetta Bernabei.
A noncommutative enumeration problem
In this article we tackle the combinatorics of coloured hard-dimer objects. This is achieved by identifying coloured hard-dimer configurations with a certain class of rooted trees that allow for an algebraic treatment in terms of noncommutative formal power series.
math-ph↗
Central Limit Theorem for Coloured Hard-Dimers
Using an averaged generating function for coloured hard-dimers, some random variables of interest are studied. The main result lies in the fact that all their probability distributions obey a central limit theorem.
math.PR↗
Coloured Hard-Dimers
An averaged generating function for coloured hard-dimers is being investigated by proving estimates for the latter. Furthermore, two different enumerating problems and their distributions are studied numerically.
math.CO↗