Random Walk of an Active Particle in a Non-Homogeneous Environment
1995, v.1, №1, 91-112
We consider the following problem. A particle performs a random walk in a non-homogeneous environment. The main feature of this random walk is that the particle can alter the environment. We will show that the behaviour of the particle in the non-critical case ``does not depend'' on the initial state of the environment. In the critical case however, the role of the initial environment is more essential. As an example, we can model a random computation on a Turing machine by a head moving right and left along an infinite tape.
Keywords: random walk,random environment,Lyapunov functions,random Turing machine