Author

J. Hermon

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Preprint Sep 2026

Random walk on the small-world network model in 3 or more dimensions

We study the mixing time of a simple random walk on the small-world network defined by adding edges to $\mathbb{Z}_n^d$ as follows: for each pair $\{x,y\}$ we add an edge with probability $Z_n/\|x-y\|^{d}$ with $Z_n$ chosen so that the average number of added edges to every vertex is $1$. When $d\geq 3$, we show that w...

Z. Baran, J. Hermon, Anđela Šarković et al. · 3 citations · ⚡1

Preprint Sep 2026

Universality of cutoff for the Exclusion Process

Under a fairly general condition on the underlying jump rates, we prove that the Exclusion Process with fixed particle density exhibits cutoff at time $t_{{mix}}\sim \frac{1}{2}{t}_{{rel}} \log N$, where $N$ is the volume and ${t}_{{rel}}$ the relaxation time of the single-particle dynamics. Our result covers, in parti...

J. Hermon, G. Kozma, Justin Salez · 0 citations