4 problems

Mean-kernel range conjecture. There exists $p_0\in(2.61,2.611)$ such that the power-Wasserstein metric of parameter $p$ is a mean kernel metric if and only if

Let $W_i=(W_i,S_i,I_i,\mathbf{\Omega}_i)$ be signed graphexes on sigma-finite Borel spaces, let $D_{\lvertW_i\rvert}>0$ everywhere, and suppose that the weak kernel distance satisf…

Let $W_i=(W_i,S_i,I_i,\mathbf{\Omega}_i)$ be signed graphexes, and let the weak kernel metric identify graphexes up to its equivalence relation. For a signed graphex $W_i$, write…

Let two graphexes be equivalent when they generate the same random graph process in law, and let a pullback be the graphex obtained by composing its components with a measurable ma…