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Let $X$ be a topological affine space over $\mathbb C$, with no additional assumptions. Let $X^*$ denote its dual space of continuous affine functionals $X \to \mathbb C$, equipped with the weak-$*$ t …

Motivation: Let $\Gamma = (V,E)$ be a directed graph. To each edge $e \in E$, choose a value $\kappa^e \in \mathbb R$, representing the cost of transporting one unit of "stuff" through the edge. Let $ …

Consider the Fréchet space $\Omega = C(\mathbb R^d)$ of real-valued continuous functions equipped with the seminorms $$\|f\|_D := \sup_{x,y \in D} \left\{ |f(x)|, \tfrac{|f(x)-f(y)|}{|x-y|} \right\}, …

Last-passage percolation is a model of random geometry on the lattice which satisfies a superadditive inequality (a reverse triangle inequality). On the lattice $\mathbb Z^2$, define a passage time $ …

A keyword that comes to mind is "first-passage percolation on the complete graph of n vertices," though I don't know that anybody's studied this. FPP is the assignment of random lengths (or "passage t …

Consider the unit sphere. Then p(π, π/2, π/2) = ∞. The north and south poles are distance π apart, and every point on the equator is distance π/2 from them. Forcing every positive real distance to …