Paper published as a letter in PRE on first-passage on disordered intervals

Alongside Sid Redner (professor at the Santa Fe Institute) I recently published an article on first-passage time processes on disordered intervals. This is an “old school” physics project, in a similar vein to work done on the Sinai model—think random walks on random intervals. We build on previous work that solves for the moments of a generalized linear chain, and solve for the generating function of the first-passage time distribution using a discrete time approach. This solution allows us to easily explore how disorder affect the moments (in particular the emergence of plateaus of similar first-passage time), see that partial ensembles from simulation based approaches can be wildly misleading and that first-passage on disordered intervals with 2 absorbing boundaries can lead to a new type of first-passage bimodality. You can also see a lay summary of our article here!