4 problems

Benjamini–Keane–Den Hollander conjecture. All pairs of sceneries on $\mathbb{Z}$ are distinguishable.

A locally $p$-biased function on the $n$-dimensional Boolean hypercube is one for which, at every vertex, the fraction of neighboring vertices where the function takes the value…

Let $n>0$ be even. Let $p=b/2^k$, where $1\leq b\leq 2^k$, $k\geq 1$ and $2^k$ divides $n$. Let $B_p^n$ be the set of non-isomorphic locally $p$-biased functions. Growth conjecture…

Let $c$ be a scenery and let $(y_0,y_1,\ldots)$ be a random-walk trajectory. Suppose that the scenery patch $c|_{[-m;m]}$ is to be reconstructed from the observed output string…