2025/10/17 by Ennaceur, Marwa, Jadlaoui, Amel · 1 citation
#05C63 _____________________________________________________________________ #2020: 81Q10 #47A10 #47B25 #Combinatorics (math.CO) #F.1.1 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #G.1.3 #G.2.2 #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2510.15546
We establish explicit operator norm bounds and essential self-adjointness criteria for discrete Hodge Laplacians on weighted graphs and simplicial complexes. For unweighted d-regular graphs we prove the universal estimate ‖\widetildeΔ1,*‖≤ 4(d-1), and we provide weighted extensions with a sharp comparability constant. These bounds apply without geometric completeness or curvature assumptions and ensure essential self-adjointness on natural cores. The approach extends to higher degrees via dual up/down degrees, and we show a unitary equivalence between skew and symmetric models on colorable complexes. For periodic lattices we complement the universal bounds with exact Floquet--Bloch constants, typically of order 2d, illustrating both the sharpness in growth and the generality of our method.