  A framework is presented for a statistical theory of neutron star glitches,
motivated by the results emerging from recent Gross-Pitaevskii simulations of
pinned, decelerating quantum condensates. It is shown that the observed glitch
size distributions cannot be reproduced if superfluid vortices unpin
independently via a Poisson process; the central limit theorem yields a narrow
Gaussian for the size distribution, instead of the broad, power-law tail
observed. This conclusion is not altered fundamentally when a range of pinning
potentials is included, which leads to excavation of the potential distribution
of occupied sites, vortex accumulation at strong pinning sites, and hence the
occasional, abnormally large glitch. Knock-on processes are therefore needed to
make the unpinning rate of a vortex conditional on the pinning state of its
near and/or remote neighbours, so that the Gaussian size distributions
resulting generically from the central limit theorem are avoided. At least two
knock-on processes, nearest- neighbour proximity knock-on and remote acoustic
knock-on, are clearly evident in the Gross-Pitaevskii simulation output. It is
shown that scale-invariant (i.e. power-law) vortex avalanches occur when
knock-on is included, provided that two specific relations hold between the
temperature and spin-down torque. This fine tuning is unlikely in an
astronomical setting, leaving the overall problem partly unsolved. A
state-dependent Poisson formalism is presented which will form the basis of
future studies in this area.
