Chung et al.'s multivariate central limit conjecture for cycle counts

For fixed $d$, let ${\mathcal{F}}_d(n)$ be the set of permutations of $\{1,\dots,n\}$ satisfying $i-d\leq\sigma(i)\leq i+1$ for every $i$, and let the number of $k$-cycles in such a permutation be recorded for $1\leq k\leq d+1$. Chung et al.'s conjecture. For fixed $d$, the joint limiting distribution of the numbers of $k$-cycles approaches a multivariate normal distribution as $n\rightarrow\infty$. This conjecture concerns the asymptotic cycle-count statistics of a family of restricted permutations and motivates the local central limit theorem developed in the paper; the supplied text does not establish whether the claim has been resolved.