5 problems

Let $R_{\mathrm{DPV}}(n,\theta)$ denote the parameter appearing in the Diophantine condition $\mathrm{DPV}(n,R)$ for an angle $\theta\in[0,2\pi)$. The paper proves, when…

Unbounded-jump random-walk conjecture. In this setup, the local version of the limit law for $V_n(1)$ is also true, and the random walk defined above is recurrent.

Simplified-model local limit conjecture. For all sufficiently large $n$, for the upper extremal point $M_n^+$ and every integer $k$,

Let $\mu$ be a measure on $(0,1]$ such that … Allow $\mu$ to have atoms and a continuous singular part, and suppose its absolutely continuous part is $g(x)\,dx$, with some…

Sznitman's conjecture. Condition $(T')$ is equivalent to ballisticity.