8 problems

Let $\mathcal{A}_N$ and $\mathcal{C}_N$ be the final states defined in the model's classification, and write $\mathbb{P}_q$ for probability under parameter $q$. Monotonicity conjec…

Let $Z_\infty^{N,\textnormal{min}}>cN$ for a constant $c$, and suppose $(\Lambda^N,E^N\cap\mathbf{Z}^N_0)$ is dense enough. Let $\mathcal{C}_N$ denote the consensus event. Consensu…

Let $q_N=q\in(0,1)$ be constant, let $Z_0^{N,\textnormal{min}}=\lfloor N/2\rfloor$, and let $E^N\subset\mathbf{Z}^N_0$. Let $\mathcal{A}_N$ denote the segregation event, and let…

Let $q_N=q\in(0,1)$ be constant, let $Z_0^{N,\textnormal{min}}=\lfloor N/2\rfloor$, and let $E^N\subset\mathbf{Z}^N_0$ represent the initial complete graph. Let $\mathcal{A}_N$ den…

Let $d\ge 1$, let $\mathcal N$ be a neighbourhood with $|\mathcal N|\ge 2$, and let $0\le q\le 1$. A spin-flip system is cancellative when its transition rates admit the cancellati…

Let $d\ge 2$, let $\mathcal N$ be a neighbourhood, and let $0<q<1$. The $q$-voter model is the spin-flip process on $\\{0,1\\}^{\mathbb Z^d}$ whose flip rates depend on the number…

Let $d\ge 2$, let $\mathcal N$ be a neighbourhood, and let $q<1$. The $q$-voter model is the spin-flip process on $\\{0,1\\}^{\mathbb Z^d}$ whose flip rates depend on the number of…

Consensus-exponent conjecture. The same exponents should hold for all smaller $\beta$ in the region