The Random Euclidean Matching is the problem of finding the optimal matching between two sets of independent random variables X1,…,Xn and Y1,…,Yn distributed in R^d with a probability density ρ. The main problem is first to minimize the quantity Cn(π):=\sum_{i=1}^n|Xi-Yπi|^p with respect to the permutations π of the indexes {1,…,n}, and then to study the expectation of the minimum of Cn(π) with respect to the probability distribution of the variables, for fixed p and d and for large n.

The object of this talk is the case of Gaussian random variables, that is, when the variables are independent and distributed in R^d with the Gaussian probability density.