Skip to main content
1 of 2
Richard Stanley
  • 50.8k
  • 14
  • 155
  • 279

For some further results of this nature, see Exercise 5.64 of Enumerative Combinatorics, vol. 2. This exercise deals with the uniform distribution on (0,1)-matrices or $(-1,1)$-matrices, but the arguments can be carried over to other distributions where the matrix entries are i.i.d. The proofs are similar to the argument in David Speyer's comment.

Richard Stanley
  • 50.8k
  • 14
  • 155
  • 279