Convergence theorems for exterior powers

• Matrix norm
• Cesàro limits for irreducible Markov chains
  • ergodic case
  • periodic case
• Symmetric tensor powers
  • symmetric tensor powers of a stochastic matrix are stochastic
• Exterior powers
• Exterior power of a stochastic matrix has norm at most 1
  • permanents via symmetric tensor powers
  • determinant minors bounded by permanent minors
  • permanent minors row sum bounded by row sum from symmetric tensor powers