Colin Defant

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20242026

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math.PR2025

Permutons from Demazure Products

Colin Defant

We construct and analyze several new families of permutons arising from random processes involving the Demazure product on the symmetric group. First, we consider Demazure products…

math.PR2025

Random Subwords and Billiard Walks in Affine Weyl Groups

Colin Defant, Pakawut Jiradilok, Elchanan Mossel

Let $W$ be an irreducible affine Weyl group, and let $b$ be a finite word over the alphabet of simple reflections of $W$ . Fix a probability $p \in (0, 1)$ . For each integer $…

math.PR2024

Random Subwords and Pipe Dreams

Colin Defant

Fix a probability $p \in (0, 1)$ . Let $s_{i}$ denote the transposition in the symmetric group $S_{n}$ that swaps $i$ and $i + 1$ . Given a word $w$ over the alphabet $\{s…