Sublinear expanders and their applications

In this survey we aim to give a comprehensive overview of results using sublinear expanders. The term sublinear expanders refers to a variety of definitions of expanders, which typically are defined to be graphs $G$ such that every not-too-small and not-too-large set of vertices $U$ has neighbourhood of size at least $\alpha \mathrm{\mid }U\mathrm{\mid }$, where $\alpha$ is a function of $n$ and $\mathrm{\mid }U\mathrm{\mid }$. This is in contrast with linear expanders, where $\alpha$ is typically a constant. :We will briefly describe proof ideas of some of the results mentioned here, as well as related open problems.