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.

DOI

https://doi.org/10.31274/etd-180810-5240

Copyright Owner

Tetiana Takhistova

Language

en

File Format

application/pdf

File Size

60 pages

Included in

Mathematics Commons

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