In the subcritical regime m = m_c(1-ε) with ε→0 and ε³n→∞, the largest component L1 satisfies L1 = (1+o_p(1)) * [2(α+2)/(α+1)] ε^{-2} log(ε³ n) for fixed α>0 (and analogous limits when α(n)→a).
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PageRank on undirected multi-type PAMs satisfies the power-law hypothesis with color-dependent exponents for finite colors under certain initial color distributions and attractiveness functions.
Derives novel scaling limit and explicit consensus probabilities for mean-field voter model with heavy-tailed waiting times, governed by extreme-value landscape of the tail index.
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Sharp Asymptotics for the Largest Component in the Subcritical Regime of Preferential Attachment Without Vertex Growth
In the subcritical regime m = m_c(1-ε) with ε→0 and ε³n→∞, the largest component L1 satisfies L1 = (1+o_p(1)) * [2(α+2)/(α+1)] ε^{-2} log(ε³ n) for fixed α>0 (and analogous limits when α(n)→a).
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Power-law hypothesis and (un)fairness of PageRank on undirected multi-type PAMs
PageRank on undirected multi-type PAMs satisfies the power-law hypothesis with color-dependent exponents for finite colors under certain initial color distributions and attractiveness functions.