On the spectral dimension of causal triangulations
ArXiv 0908.3643 (2009)
Abstract:
We introduce an ensemble of infinite causal triangulations, called the uniform infinite causal triangulation, and show that it is equivalent to an ensemble of infinite trees, the uniform infinite planar tree. It is proved that in both cases the Hausdorff dimension almost surely equals 2. The infinite causal triangulations are shown to be almost surely recurrent or, equivalently, their spectral dimension is almost surely less than or equal to 2. We also establish that for certain reduced versions of the infinite causal triangulations the spectral dimension equals 2 both for the ensemble average and almost surely. The triangulation ensemble we consider is equivalent to the causal dynamical triangulation model of two-dimensional quantum gravity and therefore our results apply to that model.Charged boundary states in a Z(3) extended minimal string
INT J MOD PHYS A 23:14-15 (2008) 2257-2259
Abstract:
In this poster, we study the boundary states of the three-state Potts model coupled to two dimensional gravity, which we call Z(3) extended minimal string. We find that two different boundary states of this model can be identified with a shift of the boundary cosmological constant. We also point out that the boundary states are classified with respect to the symmetry of the theory. This presentation is based on Ref. 1 to appear soon.The Spectral Dimension of Generic Trees
Journal of Statistical Physics 128 (2007) 1237-1260
Biased random walks on combs
ArXiv 0704.0188 (2007)
Abstract:
We develop rigorous, analytic techniques to study the behaviour of biased random walks on combs. This enables us to calculate exactly the spectral dimension of random comb ensembles for any bias scenario in the teeth or spine. Two specific examples of random comb ensembles are discussed; the random comb with nonzero probability of an infinitely long tooth at each vertex on the spine and the random comb with a power law distribution of tooth lengths. We also analyze transport properties along the spine for these probability measures.Random walks on combs
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 39:5 (2006) 1009-1037