Random Walk of an Active Particle in a Non-Homogeneous Environment

#### A.S. Gajrat

1995, v.1, №1, 91-112

ABSTRACT

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