6 problems

Let $(P_n)_n$ be a renewal covering of the natural numbers as defined in the paper. Let $Z$ be a random variable. Second-order limit conjecture. … where the convergence is in distr…

Maximality conjecture. The polynomial $Q_k$ is a maximal element of $\mathop{\mathtt{A}}_k$ and is the largest element of $\widehat{\mathop{\mathtt{A}}}_k$ for every $k\geq 3$.

Let $F$ be a displacement distribution and let $N_0$ be the random counting measure constructed from the renewal and random-walk occupation measures in the paper, with distribution…

Let $S$ be an aperiodic random walk whose increment distribution belongs to $D(\alpha,\rho)$, where $\alpha\in(0,1)$ and $\rho>0$. Let and denote the conditions stated in the sourc…

Cheliotis–den Hollander conjecture. For every $\mu_0$,

Let $F(t)$ be a distribution function on $\mathbf{R}_+=[0,\infty)$ with $F(0)=0$, and let $M(t)$ be the renewal function satisfying … A distribution on $\mathbf{R}_+$ is DFR (decre…