3 problems

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…

Maximum-law conjecture. There is a constant $c>0$ and a limiting random variable $G_d$ such that $Y_t$ converges in law to $G_d$ as $t\to\infty$, with

Let $M^{\gamma}$ be the subcritical chaos measures for $\gamma^2<2d$, and let $M^c$ be the positive random measure obtained in Proposition 3.1 as a limit…