Random walks on quasi-1d infinite structures

Abstract

In the present thesis a random walk on quasi-1d lattices as a model for transport processes on quasi-1d materials is analytically investigated. The scope of the present work is to shed light on the asymptotic behavior of basic statistical properties of the random walk on such structures�including the first and the second moments of the walker location along the structure axis, the probability of return to the starting site, the probability of ever reach a given site, the conditional mean first-passage time to a given site and the expected number of distinct sites visited.
 
 The first part of the thesis deals with developing a method for�obtaining these basic properties by employing the concepts of generating functions and the Fourier-Laplace transform. Based on this developed method, in the remaining parts, the random walks on different quasi-1d lattices, i.e., a perfect-1d lattice,�branched lattices, ladder lattices and�cylindrical lattices, and their feasible applications�are discussed.