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math.PR2026
A first order phase transition for lower tails in sparse random graphs
Byron Chin
We study the graphon variational problem that governs lower tail large deviations of the number of copies of a fixed nonbipartite graph in a sparse Erdős--Rényi random graph. O…
math.PR2025
Asymptotics for the harmonic descent chain and applications to critical beta-splitting trees
Anna Brandenberger, Byron Chin, Elchanan Mossel
Motivated by the connection to a probabilistic model of phylogenetic trees introduced by Aldous, we study the recursive sequence governed by the rule $x_n = \sum_{i=1}^{n-1} \frac{…