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arXiv · 2607.25490

An Exact Obstruction to Uniform Average Mixing on $P_{11}$

Musung Kang
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Abstract

We prove that the path $P_{11}$ does not admit uniform average mixing under any probability distribution on $\mathbb R$, answering a question of Baptista, Coutinho, and Marques in the negative. The proof is exact: we construct an explicit rational symmetric matrix $Y$ such that $\langle Y,M(t)\rangle_F=1$ for every $t\in\mathbb R$, whereas $\langle Y,J/11\rangle_F=12/11$.

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Musung Kang. 2026-07-28. An Exact Obstruction to Uniform Average Mixing on $P_{11}$. https://arxiv.org/abs/2607.25490

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