2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160317We show that the spectral gap for the interchange process (and the symmetric exclusion process) in a $d$-dimensional box of side length $L$ is asymptotic to $π^2/L^2$. This gives more evidence in favor of Aldous's conjecture that in any graph the spectral gap for the interchange process is the same as the spectral gap for a corresponding continuous-time random walk. Our proof uses a technique that is similar to that used by Handjani and Jungreis, who proved that Aldous's conjecture holds when the graph is a tree.8 pages. I learned after completing a draft of this paper that its main result had recently been obtained by Starr and ConomosProbability82C22; 60K35text