Anomalous critical and supercritical connectivity transitions

The emergence of large-scale connectivity on an underlying network or lattice, the so-called percolation phase transition, has a profound impact on the system’s macroscopic behaviours. There is thus great interest in controlling the location of the percolation transition to either enhance or delay its onset and, more generally, in understanding the consequences of such control interventions. In my talk I will report on anomalous critical and jumpy supercritical connectivity transitions that result from repeated, small interventions designed to delay the percolation transition. Models of aggregation processes ranging from random network percolation, fragmentation, the dynamics of salad dressing to DNA replication are discussed. We observe a rich phenomenology that includes non-self-averaging and stochastic Devil’s staircases.