5 problems

Extremal-process moderate-deviation conjecture. As $n\to\infty$,

Mean-regime conjecture. There exists a constant $C_{\mathrm{m}}>0$ such that, for every $y\in\mathbb{R}$,

Let $\beta>1$ and $\sigma^2=\frac{\beta}{2\beta-1}$, and let $\mathcal{N}_t^2$ be the set of type-$2$ particles at time $t$, with positions $X_u(t)$. Write $Z^{(1)}_\infty$ for the…

Let $d\geq 1$, let $\mathcal{N}_t$ be the particles at time $t$, and let $X_t(u)\in\mathbb{R}^d$ be the position of particle $u$. Define … and, for $u\in\mathcal{N}_t$, define its…

Extremal-process conjecture. In the limit of large times, the distributions of $Xi(t)$ and $Pir$ coincide: