5 problems

Let $M$ be the state manifold, let $R>0$, let $v$ denote the velocity variable, and let ${\mathcal K}$ be the interaction kernel. Let $\mu_t^N$ be the empirical measure of the norm…

Let $x_1(t),\ldots,x_N(t)$ be the trajectories of the Hamiltonian flow generated by $E^{(N)}$, and let $\delta_N((x_1(t),\ldots,x_N(t)))$ be their empirical measure. Let $\rho_t$ a…

Log-Sobolev constant limit conjecture. Under assumptions A1 and A2,

Let $v_k^n(t)$ be the random proportion of vertices at time $t$ that belong to clusters of size $k$ under the stationary law $\mathbb{P}_{\mathrm{stat}}^n$, and let…

Let $\theta$ be the bias parameter, $\theta<\text{?}$, and let $\theta$ and $\theta$ be the parameters appearing in the bias voter model on $\d^d$; for $p\a0in (0,1)$ and $t>0$, co…