  We discuss stochastic processes in the logarithmic sector of critical
cosmological topologically massive gravity. By applying a result obtained in
our previous works, we show that the logarithmic sector can be modelled as an
urn scheme, conceptualizing the random process occurring in the theory as an
evolutionary process with a dynamical state space described in terms of the
content of the urns. The urn process is then identified as the celebrated Hoppe
urn model. In this context, the "special" ball in this P\'olya-like urn
construction finds a nice interpretation as a point-like defect and gives a
concrete perspective of defect propagation in the logarithmic sector of the
theory. A Markov process encoded in the partition function is described. It is
further shown that the structure of the Markov chain consisting of a sample
space that is the set of permutations of $n$ elements, leads to a specific
description of the chain in terms of a random walk on the symmetric group. We
suggest that a possible holographic dual of LCFT could be a theory that takes
into account non-equilibrium phenomena.
