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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.

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.