1. The notion of a "duel correlation": There are two people X,Y on a square grid with some probability distribution to find them in each tile determined by the correlation matrix of X,Y, but the correlation matrix is not symmetric.
The result is that in order to find the tile which minimise the distance between X and Y, you need to pick the coordinates of the tile which has the highest probability of X and Y appearing respectively, and that tile also corresponds to the largest value in the correlation matrix of X,Y

I think the dream is using the wrong terminologies as usual. From the scenes that is shown, which has some kind of heat map on the grid, I think what is actually shown is the probability distribution of positions of X (independent of Y) $P(X)$, the probability distribution of Y (independent of X) $P(Y)$ and the optimal positions of X and Y which their distance (defined by the number of squares between them) is minimised is then given by picking the highest value of $P(X)$ and $P(Y)$
such that the entry of their correlation matrix is also maximised under the above constraints.

One possible sensible version of the above question I can think of that is based on the dream's but without all the vagueness is to simply convert this discrete problem into a continuous problem, so instead of considering positions as a integer lattice, we can consider the plane $\Bbb{R}^2$ and ask about the same question where the notion of distance is then given my the euclidean metric.
However, I am not sure if there exists a continuous version of a correlation matrix for this problem to be well defined, though