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

Musung Kang

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

Combinatorics 2026-07-28 v1

Authors: Musung Kang

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 $\langle Y,J/11\rangle_F=12/11$ .

Keywords

uniform average mixing continuous-time quantum walk path graph obstruction exact proof

Cite

@article{arxiv.2607.25490,
  title  = {An Exact Obstruction to Uniform Average Mixing on $P_{11}$},
  author = {Musung Kang},
  journal= {arXiv preprint arXiv:2607.25490},
  year   = {2026}
}

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