8 problems

Let $X^*$ be the unique capacity-achieving input distribution for the amplitude-constrained AWGN channel with peak-amplitude constraint $|X|\le A$. As $A$ increases, consider the s…

Let $k\ge2$, let $\lambda$ be sufficiently large that the mode is nonzero, and let $m_k(\lambda)$ denote a mode of the Poisson distribution of order $k$, with mean parameter…

Let $X\sim \operatorname{CMP}(\lambda,\nu)$ have probability mass function … where $\lambda,\nu>0$ and … For integer values of $\nu$, Shmueli et al. produced an approximation for…

Let $X^*$ be the capacity-achieving input distribution for the amplitude-constrained AWGN channel with peak-amplitude constraint $|X|\le A$, and let $|\operatorname{supp}(X^*)|$ de…

Let $X^*$ be the capacity-achieving input distribution for the amplitude-constrained AWGN channel with peak-amplitude constraint $|X|\le A$, and let $|\operatorname{supp}(X^*)|$ de…

Let $k\ge2$, let $\lambda$ be sufficiently large that the mode is nonzero, and let $m_k(\lambda)$ denote a mode of the Poisson distribution of order $k$, with mean parameter…

Let $G_n$ be the gain in the generalised dice game with $n\in\mathbb{N}$ equally probable faces, and define the scaled gain by … Write $h(n)=\mathbb{E}[H_n]$ for its expectation. L…

Weak-convergence conjecture. $Z_n^R$ and $Z_n^G$ converge weakly to $Z^R$ and $Z^G$ in $\ell_2$ if and only if