On the permanent of a random symmetric matrix

Let $$M_{n}$$ denote a random symmetric $$n\times n$$ matrix, whose entries on and above the diagonal are i.i.d. Rademacher variables (taking values $$\pm 1$$ with probability 1/2 each). Resolving conjecture of Vu, we prove that permanent has magnitude $$n^{n/2+o(n)}$$ $$1-o(1)$$ . Our result can also be extended to more general models matrices. In our proof, build extend some techniques introduced by Tao studying evolution permanents submatrices in matrix process.