A general law of large permanent

TL;DR

This paper establishes a general law of large permanent for doubly stochastic matrices with balanced entries, providing bounds close to the minimum and answering a question posed by Bochi, Iommi, and Ponce.

Contribution

It introduces a new law of large permanent for a broad class of matrices, extending previous understanding and addressing an open question.

Findings

Permanents of doubly stochastic matrices are close to the minimum n!/n^n

Provides bounds for large permanents in this matrix class

Answers an open question by Bochi, Iommi, and Ponce

Abstract

We show that permanents of doubly stochastic matrices with balanced entries are not far away from the minimum $n!/n^n$. As an application, we give a general law of large permanent, answering a question by Bochi, Iommi and Ponce