Erratum to: ``High order random walks: beyond spectral gap'' (Q2064755)

This short paper is an erratum to the paper [the authors, ibid. 40, No. 2, 245--281 (2020; Zbl 1463.05543)]. The authors emphasize mistakes in the original proof, false inequalities in Theorem 5.10 and the incorrect version of the Corollary 5.11. produced since they used only approximations of the eigenspaces and not the actual eigenspaces. They propose a corrected version of Theorem 5.10.