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Eigenvalue Distribution of the Laplacian on Random Complexes
We study the empirical eigenvalue distribution of a standardized up Laplacian of the Linial-Meshulam model $Y_{q+1}(n, p)$. We first give a definition of a Gaussian--semicircle law: $\mathcal{N}(0, σ^2)\boxplus \operatorname{SC}(sσ^2)$, and give a combinatorial formula of its moments in terms of pai
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