We solve an open problem concerning the relaxation time (inverse spectral gap) of the zero range process in Zd/LZd with constant rate, proving a tight upper bound of O((ρ+1)2L2), where ρ is the density of particles.
Ben Morris. "Spectral gap for the zero range process with constant rate." Ann. Probab. 34 (5) 1645 - 1664, September 2006. https://doi.org/10.1214/009117906000000304