Weak Convergence of Permanent Processes

In the previous chapter we have discussed two results on the weak convergence of random permanents in Theorems 3.4.2 and 3.4.3. The results were proved, in essence, by reducing the analysis of asymptotic behavior of a random per- manent to that of an elementary symmetric polynomial and taking advantage of the general limit theorem for elementary symmetric polynomials of increas- ing order (cf. Theorem 3.3.1). Whereas the advantage of the approach is its conceptual simplicity, we saw that it required overcoming several technical difficulties.