2003/06/11 by Nicholas Pippenger, Pippenger, Nicholas, Kristin Schleich +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry and complex manifolds #Mathematical Dynamics and Fractals #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0306049
arxiv created 2003/06/11 · openalex publication_date 2003/06/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider random topologies of surfaces generated by cubic interactions. Such surfaces arise in various contexts in 2-dimensional quantum gravity and as world-sheets in string theory. Our results are most conveniently expressed in terms of a parameter h = n/2 + χ, where n is the number of interaction vertices and χis the Euler characteristic of the surface. Simulations and results for similar models suggest that Ex[h] = log (3n) + γ+ O(1/n) and Var[h] = log (3n) + γ- π2/6 + O(1/n). We prove rigourously that Ex[h] = log n + O(1) and Var[h] = O(log n). We also derive results concerning a number of other characteristics of the topology of these random surfaces.