Eric Rowland, Hofstra University

Abstract

The Sinkhorn limit of a positive square matrix is obtained by scaling the rows so each row sum is 1, then scaling the columns so each column sum is 1, then scaling the rows again, then the columns again, and so on. It has been used for almost 90 years in applications ranging from predicting telephone traffic to machine learning. But until recently, nothing was known about the exact values of its entries. In 2020, Nathanson determined the Sinkhorn limit of a 2 x 2 matrix, and Ekhad and Zeilberger determined the Sinkhorn limit of a symmetric 3 x 3 matrix. We were able to determine the Sinkhorn limit of a general 3 x 3 matrix, and the result suggests the general form for n x n matrices. In particular, the coefficients reflect new combinatorial structure on sets of minor specifications.

This is joint work with Jason Wu.

Link to video: https://vimeo.com/1036911356?share=copy

Presented Via Zoom: https://rutgers.zoom.us/j/91865817691

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/