  We study the metastable behaviour of a stochastic system of particles with
hard-core interactions in a high-density regime. Particles sit on the vertices
of a bipartite graph. New particles appear subject to a neighbourhood exclusion
constraint, while existing particles disappear, all according to independent
Poisson clocks. We consider the regime in which the appearance rates are much
larger than the disappearance rates, and there is a slight imbalance between
the appearance rates on the two parts of the graph. Starting from the
configuration in which the weak part is covered with particles, the system
takes a long time before it reaches the configuration in which the strong part
is covered with particles. We obtain a sharp asymptotic estimate for the
expected transition time, show that the transition time is asymptotically
exponentially distributed, and identify the size and shape of the critical
droplet representing the bottleneck for the crossover. For various types of
bipartite graphs the computations are made explicit. Proofs rely on potential
theory for reversible Markov chains, and on isoperimetric results. In a
follow-up paper we will use our results to study the performance of
random-access wireless networks.
