4 problems

Small-voter-fraction nonergodicity conjecture. For every $p<1/2$, there exists a number $\beta_0(p)>0$ such that, whenever $\beta<\beta_0(p)$, the hybrid process $\tilde\eta_t$ wit…

Let $G$ be an arbitrary graph with arbitrary transition rates, let $n$ be its number of vertices, and let $\mathrm{EX}(k)$ denote the exclusion process with $k$ particles. Write…

Let $\xi$ be the exclusion-voter mixture process with parameters $\beta,p$ and state space $\mathcal{D}$. A process is recurrent from $S_0$ when…

The passage-time moment conjecture. Suppose that $p\leq1/2$ and $\beta\in[0,1]$. For any $\varepsilon>0$ and $S_0\in\mathcal{D}\setminus\{\mathcal{D}_0\}$,