11 problems

Let $({\mathcal Y}_t^\varepsilon)_{t\ge 0}$ be the fluctuation field of the directed exclusion process, with $s_\varepsilon(t)$ determined by … The field … for test functions…

Let $p_1+\dots+p_N=1$, let $a_1,\ldots,a_N>0$, and for $s\geq 1/a_1$ let $X^{(s)}$ be the infinite bin model with move distribution…

Let $u$ solve the hydrodynamic equation … with boundary parameters determined by the reservoir rates $(\alpha,\beta,\gamma,\delta)(t)$ through the relations defining $\nu_\pm(t)$.…

Let $(\xi_j)_{j\geq 1}$ be independent complex-valued random variables with distribution $\mu$, let $P_n(z)=\prod_{j=1}^n(z-\xi_j)$, and let $\mu\lsem P_n^{(k)}\rsem$ denote the em…

Reshuffling hydrodynamic-limit conjecture. Under these assumptions, the process $\phi^N_{\mathrm{RS}}(\cdot,\cdot)$ converges, in an appropriate sense, to the hydrodynamic model…

Let $T>0$, let $m$ be the porous-medium exponent, and let $g:{\mathbb T}\to[0,1]$ be measurable. For each $\kappa>0$, let…

Let $N\in\mathbb Z^+$ be the number of ball-piston pairs aligned along a one-dimensional chain, and consider the associated piston model. Spectral-gap conjecture. The spectral gap…

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…

Consider the asymmetric simple exclusion process with open boundaries, with parameters $a,b,p$ satisfying the assumptions of the paper's two-sided asymmetric regime. For…

Let $\rho0: \mathbb{R}\rightarrow[0,1]$ be an initial density profile, and let ${nu^{\epsilon}}{epsiloninmathbb{R}{0}}$ be probability measures on the configuration space…