An asymptotic approximation for the permanent of a doubly stochastic matrix

TL;DR

This paper introduces an asymptotic approximation method for calculating the permanent of doubly stochastic matrices, achieving an error of order O(n^{-1}) for certain matrix sequences.

Contribution

It provides a new determinantal approximation for the permanent with proven asymptotic accuracy for moderate-deviation matrix sequences.

Findings

Asymptotic relative error is of order O(n^{-1})

Effective for moderate-deviation matrix sequences

Advances computational approaches for permanents

Abstract

A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.