6 problems

For a coupon collector model with $N$ coupon types and positive probability vector $p=(p_1,\ldots,p_N)$, let $U_j^N$ be the number of coupon types that have appeared fewer than $j$…

Normality and convolution conjecture. The limit law for $f-E(f\mid \mathcal I)$ is normal, and the limit law for $f$ is a convolution of the limit laws for $E(f\mid \mathcal I)$ an…

Jego's conjecture. Under the setup of the source,

Let $X$ be a random walk in a cooling random environment (RWCRE) associated with a fixed $s$-canonical law and an arbitrary cooling map. Theorem gives limits of the form … where…

Gaussian distribution conjecture. As $q\to\infty$ among primes, the values

Let $p\geq 1$, and let $Y_{n,p}$ and $\sigma_{n,p}$ denote the process and normalizing sequence defined in the paper. Limsup conjecture. … This conjecture would identify the optima…