ABSTRACT

We analyze a random process in a random media modeling the motion of DNA nanomechanical

walking devices. We consider a molecular spider restricted to a well-dened one-dimensional

track and study its asymptotic behavior in an i. i. d. random environment. The spider walk is

a continuous time motion of a finite ensemble of particles on the integer lattice with the jump

rates determined by the environment. The particles mutual location must belong to a given

finite set of congurations L; and the motion can be alternatively described as a random walk

on the ladder graph Z x L in a stationary and ergodic environment. Our main result is an

annealed central limit theorem for this process. We believe that the conditions of the theorem

are close to necessary.