LAUSR

DOI: https://doi.org/10.1090/noti2255 physicists who appreciatemathematical beauty), the physicallymotivatedmodels aremathematically appealing, and have rich combinatorial structure. The third reason is that it is just a really fun research topic. The most fundamental model is the self-avoiding walk [Flo49,MS93], which is a walk that starts at the origin of a lattice and moves successively to neighboring sites, with the rule that self-intersections are forbidden. An example of a self-avoiding walk on the square lattice is shown in Figure 1, together with a self-avoiding polygon, which is a walk that returns to the origin but is otherwise self-avoiding. Formally, an n-step self-avoiding walk on Zd is a mapping ω ∶ {0, 1, ... , n} → Zd with ω(0) at the origin, steps of