Polynomial mixing conjecture for repelling random walks

Let $n$ particles evolve according to the Attracting Random Walks (ARW) model on an arbitrary graph, with interaction parameter $\beta<0$. The mixing time is measured with respect to the resulting Markov chain on the model's state space. Polynomial mixing conjecture. For all $\beta<0$ and any graph, the mixing time of the ARW model is polynomial in $n$. The conjecture formalizes the expectation that repulsive interactions prevent hard-to-escape subsets and lead to efficient mixing; simulations suggest behavior approaching independent random walks near $\beta=0$ and an even spread for very negative $\beta$.