  After reviewing the behavioral studies of working memory and of the cellular
substrate of the latter, we argue that metastable states constitute candidates
for the type of transient information storage required by working memory. We
then present a simple neural network model made of stochastic units whose
synapses exhibit short-term facilitation. The Markov process dynamics of this
model was specifically designed to be analytically tractable, simple to
simulate numerically and to exhibit a quasi-stationary distribution (QSD).
Since the state space is finite this QSD is also a Yaglom limit, which allows
us to bridge the gap between quasi-stationarity and metastability by
considering the relative orders of magnitude of the relaxation and absorption
times. We present first analytical results: characterization of the absorbing
region of the Markov process, irreducibility outside this absorbing region and
consequently existence and uniqueness of a QSD. We then apply Perron-Frobenius
spectral analysis to obtain any specific QSD, and design an approximate method
for the first moments of this QSD when the exact method is intractable. Finally
we use these methods to study the relaxation time toward the QSD and establish
numerically the memorylessness of the time of extinction.
