Author

Zhen-Yuan Zhang

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Preprint Oct 2026

Quenched First-Passage Asymptotics for Branching Random Walk on a Hamming Cube

We study continuous-time supercritical branching random walks in space-inhomogeneous random environment on the Hamming cube $\{0,1,\dots,b-1\}^d$, where the reproduction laws at each site are i.i.d. sampled. This serves as an idealized model for RNA sequence evolution with mutation--selection balance. The reproduction...

Jose H. Blanchet, Zhen-Yuan Zhang · 0 citations

Preprint Jul 2026

Precise cover times for branching random walks on Hamming graphs: (iterated) logarithmic corrections

We prove tight asymptotics of the cover time $\tau_{\mathrm{cov}}(d)$ of a continuous-time branching random walk on the Hamming graph $\{0,1,\dots,b-1\}^d$, as $d\to\infty$. We focus on the slow-branching regime, where particles move at rate one and branch at rate $\lambda\in(0,1)$. For $b>2$, we show that $\tau_{\math...

Zhen-Yuan Zhang · 0 citations