8 problems

Let $F_k(m,n)$ denote the expected cost of an optimal $k$-assignment in an $m\times n$ matrix of independent exponentially distributed random variables with mean $1$. Here a $k$-as…

Let $Z$ be a finite set of matrix positions, and let $F_{k,Z}(m,n)$ be the expected cost of an optimal $k$-assignment in an $m\times n$ matrix with zeros in the positions in $Z$ an…

Let $C_{n,n,n}$ denote the minimum cost of a perfect matching in the random $n$ by $n$ bipartite matching model, and let $\overset{\mathcal{D}}{\longrightarrow}$ denote convergence…

Connected bipartite $\kappa$-factor conjecture. The connected bipartite $\kappa$-factor problem should allow for a similar analysis to that developed for the concave one-dimensiona…

Let $(X_{ij})$ be an $n\times n$ random matrix with independent entries having common distribution $\mathcal{P}$, let $\mathcal S_n$ be the group of permutations of…

Let $\Omega$ be a regular two-dimensional manifold, and let $E_{\Omega}(N)$ be its expected optimal assignment cost. Let $R_{\Omega}$ denote its Robin mass. Universal-function and…

Let $\Omega$ and $\Omega'$ be regular two-dimensional manifolds. Define the Robin masses by … Under the assumption that regularization by the parameter $\delta$ acts in the same wa…

Non-uniform-density conjecture. The same asymptotic relation should hold when the points are generated from non-uniform densities.