  Empirical data reveals that the liquidity flow into the order book
(depositions, cancellations andmarket orders) is influenced by past price
changes. In particular, we show that liquidity tends todecrease with the
amplitude of past volatility and price trends. Such a feedback mechanism inturn
increases the volatility, possibly leading to a liquidity crisis. Accounting
for such effects withina stylized order book model, we demonstrate numerically
that there exists a second order phasetransition between a stable regime for
weak feedback to an unstable regime for strong feedback,in which liquidity
crises arise with probability one. We characterize the critical exponents,
whichappear to belong to a new universality class. We then propose a simpler
model for spread dynamicsthat maps onto a linear Hawkes process which also
exhibits liquidity crises. If relevant for thereal markets, such a phase
transition scenario requires the system to sit below, but very close tothe
instability threshold (self-organised criticality), or else that the feedback
intensity is itself timedependent and occasionally visits the unstable region.
An alternative scenario is provided by a classof non-linear Hawkes process that
show occasional "activated" liquidity crises, without having to bepoised at the
edge of instability.
