7 problems

Random Runge approximation conjecture. There is a sequence $R_k(\omega,z)$ of random rational functions such that, for each $\omega$, $R_k(\omega,\cdot)\rightarrow f(\omega,\cdot)$…

Let $f_{\text{\sc ise}}$ be the density of the integrated super-Brownian excursion (ISE), whose existence and Hölder continuity are established in the paper. ISE density differenti…

Let $w,w'$ be two words, and let $\tilde{c}(w)$ denote the second auto-correlation constant defined by the asymptotic second moment of the number of leaves associated with $w$. The…

Let $(X(k))_{k \geqslant 1}$ be a sequence of independent random variables uniform on $\{\pm 1\}$, and define $(A(N))_{N \geqslant 0}$ by the paper's formal power series. For any f…

Let $(A(N))_{N \geqslant 0}$ be defined by the same formal power series from a sequence $(X(k))_{k \geqslant 1}$. Real-Gaussian and Rademacher extension conjecture. The first-momen…

Let $(A(N))_{N \geqslant 0}$ be defined by the formal power series associated with a sequence $(X(k))_{k \geqslant 1}$ of independent standard complex Gaussians. First-moment asymp…

Let $K_1$, $K_2$, and $k$ be random compact subsets of $\mathbb C$ with $K_1(\omega)\cap K_2(\omega)=\emptyset$ for every $\omega$. Assume … Let…