7 problems

Let $\mu$ be a probability distribution on the non-negative integers satisfying … Let $(\mathscr{G}_n)_{n\in\mathbb{N}}$ be configuration graphs on $n$ vertices derived from $\mu$,…

Consider the long-range contact process (LoRaC) on the spatial model of the paper, with edge length $|y-x|$ and a parameter $\alpha>0$. Fewer edges. The LoRaC has a phase transitio…

Let $q^{(t)},p\in(0,1)$ be given and let $\alpha>1$. Let $q^{(x)}$ denote the parameter controlling the sparse spatial environment in the long-range contact process (LoRaC). Extinc…

Let $q^{(t)},q^{(x)},p\in(0,1)$ be given, and let $\alpha>1$. The long-range contact process (LoRaC) is the percolation model described in the paper, with edges whose length distri…

Positive critical-rate conjecture. For every $\gamma>0$ and $q\in[0,1]$,

Fast-update limit conjecture.

Critical branching-rate conjecture. In the general model,