7 problems

Let $\Lambda$ be an $\operatorname{ASL}_d(\mathbb R)$-invariant point process with distribution $\mu$. Let $\mathcal{M}(\mathbb R^d)$ denote the space on which the point-process di…

Let $f\in L^2_{\operatorname{imp}}$, let $(A_k)$ be pairwise disjoint Borel subsets of $\mathbb R_+$, and define $f_k=f\mathbf 1_{A_k}$. Let $(S_n)$ be the arrival times of a Poiss…

Let $\mathscr C$ denote the class of functions for which the Poisson series under consideration has the required convergence properties, and let an affine transformation of the var…

Let $N$ be a Poisson random measure and let $L^2_{\operatorname{imp}}$ be the space of bounded, square-integrable functions for which the relevant improper integrals exist. For a f…

Let $V$ be a set with one Poisson particle source for each element, and let a degree-$r$ arrival experiment receive particles in successive batches of $r$, silencing each source af…

Let $X^\lambda$ be a homogeneous Poisson point process on $\mathbb{R}^2$, so that $\Lambda\equiv |\cdot|$, and let $g_{(\gamma,N_0,\tau)}(X^\lambda)$ be the SINR graph with noise p…

Let $F$ be an absolutely continuous displacement distribution, let $\lambda>0$, and let $B\in\mathcal{B}_b(\operatorname{\mathbb{R}})$. Let $N^{(g)}$ and $\lambda^{(g)}$ be defined…