Limiting Distributions and Deviation Estimates of Random Walks in Dynamic Random Environments

This dissertation includes my research works during Ph.D. career about three different kinds of random walks in (dynamical) random environments. It includes my two published papers “Functional weak limit of random walks in cooling random environments” [1] which has been published in electronic communications in probability in 2020, and “Variable speed symmetric random walk driven by the simple symmetric exclusion process” [2] which is the joint work with Peterson and Menezes and has been published in electronic journals of probability in 2021. This dissertation also includes my two other projects, one is the joint work with Janjigian and Emrah about moderate deviation and exit time estimates in integrable directed polymer models. The other one is the joint work with Peterson and Conrado that extends the weak limit of random walks in cooling randon environments with underlying environment is in the transient case with parameter κ ∈ (0, 1) or κ = 2. Previous results show the weak limit in the cases where the environment is recurrent or transient but with κ \u3e 2 or κ ∈ (1, 2)