Full Resolution to Papikian's Conjecture

2025/10/16 by Vollrath, Paul
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.15161

Abstract

We prove Papikian's conjecture on the spectrum of the signed up-down walk on the spherical building. Namely, we show that in the spherical building of dimension n-2 and thickness q + 1, the number of distinct eigenvalues is independent of q and for q going to infinity the positive eigenvalues converge to n-1, ... , n-i.

Citations

• Asymptotic behavior of Laplacian eigenvalues of subspace inclusion graphs
• High Order Random Walks: Beyond Spectral Gap
• Bounded Degree Cosystolic Expanders of Every Dimension

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