In this talk, I will introduce the random wave conjecture for Maass forms on the modular surface, and present some results on the quantum unique ergodicity, the L^4 norm, and the cubic moment of Hecke-Maass cusp forms. I will also discuss the joint distribution of Maass forms. The proofs use the analytic theory of L-functions. (Based on joint work with Shenghao Hua and Liangxun Li.)
