Expected volume of intersection of Wiener sausages and heat kernel norms   on compact Riemannian manifolds with boundary
  Estimates are obtained for the expected volume of intersection of independent Wiener sausages in Euclidean space in the small time limit. The asymptotic behaviour of the weighted diagonal heat kernel norm on compact Riemannian manifolds with smooth boundary is obtained in the small time limit 
M.van den Berg and P.Gilkey