6 problems

LLL mixing and density conjecture. (i) The sequence $(|\mu_{k(i)}|)_{i=1,2,\ldots}$ is strongly mixing as a stochastic process. (ii) Each $|\mu_{k(i)}|$ is contained in a compact s…

Summability conjecture. The assumption that the $\phi$ rates are summable can be dropped; that is, the potential well should remain uniformly bounded away from $0$ for $\phi$-mixin…

Weak-condition block bootstrap conjecture. The block bootstrap might be established under non-stationarity using the same weak moment and mixing conditions as the subsampling estim…

Convolved subsampling conjecture. Convolved subsampling might provide a route for establishing the block bootstrap under minimal conditions for non-stationary, strongly mixing proc…

Generic chaining conjecture. The same issue is conjectured to arise for the generic chaining argument by Talagrand (2005).

Fan–Yao conjecture. Similar asymptotic distributional results for $\Delta_n$ should hold when $(X_i)$ is stationary and satisfies certain mixing conditions.