A shift from democratic to tri-bimaximal neutrino mixing with relatively large θ13

Recent neutrino oscillation data hint that the smallest neutrino mixing angle θ13 is possible to lie in the range 5°≲θ13≲12°. We show that reasonable perturbations to the democratic mixing pattern, which is geometrically related to the tri-bimaximal mixing pattern through an equal shift θ⁎≃9.7° of two large mixing angles, can naturally produce a nearly tri-bimaximal neutrino mixing matrix V with sufficiently large θ13. Two especially simple but viable scenarios of V are proposed and their phenomenological consequences are discussed.