A closed formula for the asymptotic expansion of the Bergman kernel
  We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants. The proof relies on a combinatorial interpretation of a recursive formula due to M. Englis and A. Loi. 
Hao Xu
math.DG math-ph math.MP