Degree Type

Thesis

Date of Award

2017

Degree Name

Master of Science

Department

Mathematics

Major

Applied Mathematics

First Advisor

Alex Roitershtein

Abstract

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.

Copyright Owner

Tetiana Takhistova

Language

en

File Format

application/pdf

File Size

60 pages

Included in

Mathematics Commons

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