Analysis of a class of recursive distributional equations including the resistance of the series-parallel graph

2025/11/14 by Morfe, Peter S. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2511.11036

Abstract

This paper analyzes a class of recursive distributional equations (RDE's) proposed by Gurel-Gurevich [17] and involving a bias parameter p, which includes the logarithm of the resistance of the series-parallel graph. A discrete-time evolution equation resembling a nonlinear, fractional Fisher-KPP equation is derived to describe the CDF's of solutions. When the bias parameter p = (1)/(2), this equation is shown to have a PDE scaling limit, from which distributional limit theorems for the RDE are derived. Applied to the series-parallel graph, the results imply that N^-1/3 log R^(N) has a nondegenerate limit when p = (1)/(2), as conjectured by Addario-Berry, Cairns, Devroye, Kerriou, and Mitchell [1].

Cited by

• Hipster random walks, random series-parallel graph and random homogeneous systems

Related

• Hipster random walks, random series-parallel graph and random homogeneous systems
• A new relationship between Erdős-Rényi graphs, epidemic models and Brownian motion with parabolic drift
• On limiting distributions of Graham, Knuth, Patashnik recurrences
• A recursive distribution equation for the stable tree
• The noisy veto-voter model: a Recursive Distributional Equation on [0,1]