4 problems

Let $V\subseteq\mathbb{R}$ with $|V|=n$, and let the known distances be distributed as in $G(V,\lambda/n)$ for a parameter $\lambda>0$. Call a subset reconstructible if every injec…

Friedgut–Kalai conjecture. There is an absolute constant $c$ such that, if $up^n(P)\epsilon$, then

For the ring puzzle, let $p_{\epsilon}(n)$ be the unique value of $p$ such that the probability that the jigsaw process solves the puzzle is $f0a0\epsilon$, for fixed…

Let $S_n=[0,\sqrt{n}]\times[0,\sqrt{n}]\subset\mathbb{R}^2$, place points in $S_n$ according to a Poisson process of intensity $1$, and join each point to its $k$ nearest neighbour…