Random walks in Markovian environments: a perturbative approach

Random Walks (RWs) in Random Environments (REs) are RWs with random transition kernels given as a function of a random field or a random process (the RE).
These are central models in the theory of disordered systems that have applications in various applied fields such as bio-mathematics, physics, chemistry and economics.
In the first part of this talk I will give an overview of the state of the art on the integer lattice by considering a simple example both in static (frozen) and dynamic (evolving) media.
The second part of the talk will focus on some recent works, jointly with O. Blondel (Lyon) and A. Faggionato (Rome), where we derive limit theorems for a certain class of RWs in Markovian REs in a perturbative regime.