Theoretical results for random forests?
I guess you already had a look at Breiman's 2001 paper about RF. I can just point out a few other references: 

Empirical comparisons of different RF simplifications that allow proving theorems:  Narrowing the Gap: Random Forests In Theory and In Practice 

This is the newest reference I can provide. In this paper you can also find some citations of Biau's papers about initial work on theoretical results for RF.

If you are interested in theoretical results about variable importance in RF: Understanding variable importances in forests of randomized trees

Actually I just found out that last paper's author (Gilles Louppe) just posted on arxiv his PhD thesis (v2): Understanding Random Forests: From Theory to Practice