Portrait of the String as a Random Walk

In this paper we analyze a Rutherford type experiment where light probes are inelastically scattered by an ensemble of excited closed strings, and use the corresponding cross section to extract density-density correlators between different pieces of the target string. We find a wide dynamical range where the space-time evolution of typical highly excited closed strings is accurately described as a convolution of brownian motions. Moreover, we show that if we want to obtain the same cross section by coherently scattering probes off a classical background, then this background has to be time-dependent and singular. This provides an example where singularities arise, not as a result of strong gravitational self-interactions, but as a byproduct of the decoherence implicit in effectively describing the string degrees of freedom as a classical background.