3 problems

Let $\mu$ be a probability measure on $\mathbb{C}$, let $X_1,X_2,\ldots$ be independent and identically distributed with law $\mu$, and define $P_n(z)=\prod_{j=1}^n(z-X_j)$. Let ……

Let $(\xi_n)_{n\geq 1}$ be i.i.d. random variables satisfying … and let $\alpha>0$ satisfy … For a given sequence $(S_n)_{n\geq 0}$, consider the stochastic difference equation … H…

Fix a connected multicyclic graph $H$ with $2$-core $H'$, and let $t$ be the number of vertices in $H\setminus H'$. For a fixed $m\geqslant m_H$, let $W_n$ and $W'_n$ denote the nu…