Date of Award
Master of Science
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.
Takhistova, Tetiana, "Spider walk in a random environment" (2017). Graduate Theses and Dissertations. 15626.