We construct the pair of logarithmic operators associated with the recoil of a D-brane. This construction establishes a connection between a translation in time and a world-sheet rescaling. The problem of measuring the centre of mass coordinate of the D-brane is considered and the relation between the string uncertainty principle and the logarithmic operators is discussed.

No abstract

Abstract. We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.1 durhuus@math.ku.dk 2 thjons@raunvis.hi.is

Abstract. We define generic ensembles of infinite trees. These are limits as N → ∞ of ensembles of finite trees of fixed size N, defined in terms of a set of branching weights. Among these ensembles are those supported on trees with vertices of a uniformly bounded order. The associated probability measures are supported on trees with a single spine and Hausdorff dimension d h = 2. Our main result is that their spectral dimension is d s = 4/3, and that the critical exponent of the mass, defined as the exponential decay rate of the two-point function along the spine, is 1/3.

No abstract