I will tell about a long story in interacting particle systems that emerged across decades in several stages:
1. A second class particle in asymmetric exclusion (ASEP) and in an exponential bricklayers process (EBPL) sees certain shock-like distributions stationary.
2. Such shock-like distributions perform a simple random walk in both ASEP and EBLP (what does that mean…?)
3. It is in fact the second class particle in the middle of the shock that does the random walk (what does THIS mean…?). Besides ASEP and EBLP, it also works for an exponential zero range process (EZRP).
4. Q-zero range is yet another example that has this random walking property. The second class particle really helps to reveal this secret here.
The last step is recent, the ones before are old results.
(Joint work with Gyorgy Farkas, Peter Kovacs, Attila Rakos; Lewis Duffy, Dimitri Pantelli)