Sandpile groups and the coeulerian property for random directed graphs

TL;DR

This paper investigates the properties of sandpile groups in random directed graphs, calculating the distribution of their Laplacian cokernels and establishing bounds on the probability of coeulerian structures.

Contribution

It introduces a method to analyze the cokernel distribution of Laplacians in random digraphs and provides asymptotic bounds on coeulerian probabilities.

Findings

Probability that a random digraph is coeulerian is asymptotically at most 0.43.

Distribution of Laplacian cokernels in random directed graphs is characterized.

Methodology extends previous work to directed graph structures.

Abstract

We consider random directed graphs, and calculate the distribution of the cokernels of their laplacian, following the methods used by Wood. As a corollary, we show that the probability that a random digraph is coeulerian is asymptotically upper bounded by a constant around $0.43$.