9 problems

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…

Consider a zero-range process on $L$ vertices with inhomogeneous rates … where $\lambda_x\in[a_1,a_2]$ for constants $0<a_1<a_2<\infty$, and where $c(\cdot)$ satisfies (H.1) and (H…

Dirichlet hydrodynamic-limit conjecture. For $\theta<1$, the empirical density should be described in the hydrodynamic limit by this equation with Dirichlet boundary conditions.

Consider a zero-range process on a fixed graph $G$ with $N>0$ particles and interaction parameter $alpha>1$, whose level-two large-deviation rate function is denoted by…

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 $\rho$ 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…

Existence conjecture. Under suitable assumptions, the construction of the dynamics can be established so as to validate the existence of the product stationary blocking measures…

Let $|q|<1$ and $| u|<1$. Let $N$ be a positive integer, and let $mathbf{x}=(x1leqdotsleq xN)$ and $mathbf{y}=(y1leqdotsleq yN)$ be arbitrary $N$-tuples of integers. Suppose the en…