An $\mathsf{\epsilon}$ -expansion for small-world networks

Abstract

I construct a well-defined expansion in $\epsilon=2-d$ for diffusion processes on small-world networks. The technique permits one to calculate the average over disorder of moments of the Green's function, and is used to calculate the average Green's function and fluctuations to first non-leading order in $\epsilon$, giving results which agree with numerics. This technique is also applicable to other problems of diffusion in random media.