  Homochirality, i.e. the dominance across all living matter of one enantiomer
over the other among chiral molecules, is thought to be a key step in the
emergence of life. Building on ideas put forward by Frank and many others, we
proposed recently one such mechanism in G. Laurent et al., PNAS (2021) based on
the properties of large out of equilibrium chemical networks. We showed that in
such networks, a phase transition towards an homochiral state is likely to
occur as the number of chiral species in the system becomes large or as the
amount of free energy injected into the system increases. This paper aims at
clarifying some important points in that scenario, not covered by our previous
work. We first analyze the various conventions used to measure chirality,
introduce the notion of chiral symmetry of a network, and study its
implications regarding the relative chiral signs adopted by different groups of
molecules. We then propose a generalization of Frank's model for large chemical
networks, which we characterize completely using methods of random matrices.
This analysis can be extended to sparse networks, which shows that the
emergence of homochirality is a robust transition.
