Conditioning random points by the number of vertices of their convex hull: the bi-pointed case

Jean-François Marckert, Ludovic Morin

Pick $N$ random points $U_1,\cdots ,U_N$ independently and uniformly in a triangle ABC with area 1, and take the convex hull of the set $\{A,B,U_1,\cdots ,U_N\}$. The boundary of…