7 problems

Beijeren–Kutner–Spohn conjecture. Based on mode-coupling theory, the diffusion coefficient satisfies $D(t)\sim(\log t)^{2/3}$ in dimension $d=2$ and $D(t)\sim t^{1/3}$ in dimension…

Let the asymmetric simple exclusion process be the Markov process on $\{0,1\}^{\mathbb Z^d}$ in which particles jump with asymmetric rates, subject to the exclusion rule that each…

Coarsening conjecture. The linear behavior of $j^\ast(\rho)$ in this regime does not result from an effective absence of interactions. Instead, the dynamics exhibits coarsening: th…

Let $q\in(0,1)$ and let $n$ be the parameter determining the one-species jump rates. Define … Consider the type $D$ ASEP with parameters $(2,0)$ and $(3,0)$ on the infinite lattice…

Consider the asymmetric simple exclusion process on a segment of size $N$ with open boundaries, in which particles have a drift, may move in both directions within the segment, and…

The asymmetric simple exclusion process (ASEP) and the totally asymmetric simple exclusion process (TASEP) are stochastic particle systems whose Bethe ansatz gives their eigenvalue…

Let $pin(1/2,1]$ and write $\rho=2p-1$. Consider the asymmetric simple exclusion process (ASEP), with particles jumping right at rate $p$ and left at rate $1-p$, and let $X_0(t)$ d…