${\ell }^p$-distortion and $p$-spectral gap of finite regular graphs

Pierre-Nicolas Jolissaint, Alain Valette

We give a lower bound for the ${\ell }^p$-distortion $c_p(X)$ of finite graphs $X$, depending on the first eigenvalue ${\lambda }_1^{(p)}(X)$ of the $p$-Laplacian and the maximal displacement…