8 problems

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…

Let $F_{k,m,n}(t)=\mathbb{E}(\exp(t\cdot C_{k,m,n}))$ be the moment generating function of the minimum cost $C_{k,m,n}$ of a $k$-matching in the random bipartite matching model. Ze…

Let $C_{k,m,n}$ be the minimum cost of a $k$-matching in the random bipartite matching model, and let its cumulants $\kappa_p$ be defined by … where…

Caracciolo–Parisi–Sicuro conjecture. The limit equals

Benedetto–Caglioti conjecture. The above limit holds with value

Let $d\geq 3$, let $(X_i)_{i\geq 1}$ and $(Y_i)_{i\geq 1}$ be independent uniform random variables on $[0,1]^d$, and let $W_{Q_1}$ denote the Wasserstein matching cost on the unit…

Let $d$ be the dimension, let $f^{\mathrm{ref}}(L)$ denote the rescaled expected cost of matching a random point measure with the reference measure on a cube of side length $L$, an…

Let $G$ be a $d$-regular bipartite graph on $2N$ vertices, where $d=d(N)\to\infty$ as $N\to\infty$. Assign to each edge $e$ an independent exponential random variable with rate $1$…