Large deviations for branching process in random environment

We will consider a version of Galton-Watson process called the branching process in random environment, describing a population growth where the individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We will focus on large deviations for the process in question. If time allows we will investigate the corresponding first passage time.  The talk is based on a joint work with Dariusz Buraczewski available at https://arxiv.org/abs/1706.03874