4 problems

Let $Q^N$ be the law on $\mathcal D([0,T],\mathcal M_+)$ of the empirical process $\{\pi_t^N:t\in[0,T]\}$. Let $\rho:[0,T]\times[0,1]\to\mathbb R_+$ be a weak solution of the hydro…

Let $I_N$ be the lattice site set, let $\Omega_N$ be the configuration space, and let $\{\mu^N\}_{N\in\mathbb N}$ be probability measures on $\Omega_N$ satisfying…

Let $\rho$ be the particle density, let $h$ be the critical density, let $\phi_{\pi(n)}(\rho;n)$ be the finite-$n$ flux in the zero-range model with parameter $\pi(n)$, and let…

Consider an inhomogeneous zero-range process with $n$ sites, rate functions $r_i$, particle number $m$, and site weights $p=(1/n,\ldots,1/n)$. Assume that there are constants…