Large-scale structure as a critical phenomenon

We present an analytical theory for the spatial distribution of energetically soft domain walls produced in cosmological phase transitions. It is shown that this distribution is well described by statistical percolation theory where the probability parameter p is smaller than the critical probability pc. We discuss, in detail, the nonequilibrium phase transition that triggers the formation of domain walls. We then briefly describe two applications of these ideas, the first to the formation of the Abell clusters and voids and the second to the energy density fluctuations generated during a generic predecoupling phase transition.