v 1 1 1 Ju n 20 03 Topological Characteristics of Random Surfaces Generated by Cubic Interactions
نویسنده
چکیده
We consider random topologies of surfaces generated by cubic interactions. Such surfaces arise in various contexts in 2-dimensional quantum gravity and as worldsheets of 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 χ is 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] = logn + O(1) and Var[h] = O(logn). We also derive results concerning a number of other characteristics of the topology of these random surfaces. * The work reported here was supported by an NSERC Research Grant and a Canada Research Chair. † The work reported here was supported by an NSERC Research Grant.
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تاریخ انتشار 2008