The Concentration of the Product of Exponentials Around the Exponential of the Sum

For two matrices A and B, and large n, we show that most products of n factors of and n factors of are close to . This extends the Lie-Trotter formula. The elementary proof is based on the relation between words and lattice paths, asymptotics of binomial coefficients, and matrix inequalities. The re...

Full description

Saved in:
Bibliographic Details
Published in:The American mathematical monthly 2023-07, Vol.130 (6), p.503-514
Main Authors: Anshelevich, Michael, Pritchett, Austin
Format: Article
Language:English
Subjects:
Binomial coefficients
Mathematical problems
Matrix
Proof theory
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For two matrices A and B, and large n, we show that most products of n factors of and n factors of are close to . This extends the Lie-Trotter formula. The elementary proof is based on the relation between words and lattice paths, asymptotics of binomial coefficients, and matrix inequalities. The result holds for more than two matrices.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2023.2185036