Deepesh Singhal

Distribution of Sandpile groups of random bipartite graphs

Fix a prime $p$ and a constant $\frac{1}{p}<\alpha\leq 1$. Consider the random Erd\H{o}s--R\'enyi bipartite graph $G_{\alpha}(n,u)$ with bipartition $(V_1,V_2)$ of sizes $|V_1|=n$ and $|V_2|=\lceil\alpha n\rceil$, and edge probability $0<u<1$. The authors of [1] and [8] conjectured a limiting distribution for the $p$-S...