Uniform-edge conjecture for the expected maximum matching in random bipartite graphs

Let $K_{n,n}$ be the complete bipartite graph with $n$ vertices on each side. A fractional bipartite matching is a collection of edge probabilities $x=(x_{uv})$ satisfying the vertex constraints $\sum_v x_{uv}=1$ and $\sum_u x_{uv}=1$. Let $R(x)$ be the random bipartite graph in which each edge $(u,v)$ appears independently with probability $x_{uv}$. Equivalently, let $A=(a_{ij})$ be a doubly stochastic $n\times n$ matrix, with $x_{uv}=a_{ij}$ for corresponding vertices. Uniform-edge conjecture. The expected size of the maximum matching in $R(x)$ is minimized when $x_{uv}=1/n$ for every edge. Equivalently, for a random bipartite graph whose edge $(i,j)$ appears independently with probability $a_{ij}$, the expected maximum matching size is minimized when $a_{ij}=1/n$ for all $(i,j)$. The uniform instance is known to have expected maximum matching size $(\gamma+o(1))n$, where $\gamma=2(1-\lambda)-\lambda^2$ and $\lambda=e^{-\lambda}$; the conjecture asserts that this instance is worst among all fractional matchings in $K_{n,n}$.