3 problems

Spohn's conjecture. The equilibrium fluctuations of the current should converge in the limit to a $1/4$ fractional Brownian motion.

Let $S$ be a finite set, let $r:S\times S\to[0,\infty)$ be symmetric, and let $J_i^\pm,J_i^0$ and $K_i^\pm,K_i^0$ be the operators on the symmetric exclusion process defined by ……

Consider the symmetric exclusion process on $\mathbb{Z}$ with translation-invariant transition probabilities describing a random increment whose distribution lies in the domain of…