Numerical estimation of the Hausdorff dimension of D-random feuilletages

2025/11/06 by Castro, Alicia, Tanasa, Adrian
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2511.04519

Abstract

We implement numerical techniques to simulate D-random feuilletages, candidates for higher-dimensional random geometries introduced in L. Lionni and J.-F. Marckert, Math. Phys. Anal. Geom. 24 (2021) 39. Using finite-size scaling techniques, our approach allows to give a numerical estimation of the Hausdorff dimension d_H of these feuilletages. The results obtained are compatible with the formal result known for the Brownian map, which corresponds to the D=2 random feuilletage. For the D=3 case, our numerical study finds a good agreement with the conjectured value d_H=8.

Citations

• Phases of Tree-decorated Dynamical Triangulations in 3D
• Random Riemannian Geometry in 4 Dimensions
• Tightness of exponential metrics for log-correlated Gaussian fields in arbitrary dimension
• A family of triangulated 3-spheres constructed from trees
• Models of random subtrees of a graph
• Iterated foldings of discrete spaces and their limits: candidates for the role of Brownian map in higher dimensions
• Liouville quantum gravity as a mating of trees
• The Brownian map is the scaling limit of uniform random plane\n quadrangulations
• Scaling limits of random trees and planar maps
• Liouville Quantum Gravity and KPZ

Related

• Hausdorff dimension of fermions on a random lattice
• Hausdorff dimension of random limsup sets of balls in the unit cube
• The Hausdorff Dimension of Two-Dimensional Quantum Gravity
• Hausdorff dimension of certain random self--affine fractals
• Iterated foldings of discrete spaces and their limits: candidates for the role of Brownian map in higher dimensions