On the randomized Horn problem and the surface tension of hives

Aalok Gangopadhyay, Hariharan Narayanan

Given two nonincreasing $n$-tuples of real numbers $\hat{I}{»}_n$, $\hat{I}{¼}_n$, the Horn problem asks for a description of all nonincreasing $n$-tuples of real numbers $\hat{I}{½}_n$ such that there ex…