Repository: Freie Universität Berlin, Math Department

Transition Path Theory for Markov Jump Processes

Metzner, Ph. and Schütte, Ch. and Vanden-Eijnden, E. (2009) Transition Path Theory for Markov Jump Processes. Mult. Mod. Sim., 7 (3). pp. 1192-1219.

[img] PDF - Published Version
Restricted to Registered users only
Available under License Creative Commons Attribution Non-commercial.


Official URL:


The framework of transition path theory (TPT) is developed in the context of continuous-time Markov chains on discrete state-spaces. Under assumption of ergodicity, TPT singles out any two subsets in the state-space and analyzes the statistical properties of the associated reactive trajectories, i.e., those trajectories by which the random walker transits from one subset to another. TPT gives properties such as the probability distribution of the reactive trajectories, their probability current and flux, and their rate of occurrence and the dominant reaction pathways. In this paper the framework of TPT for Markov chains is developed in detail, and the relation of the theory to electric resistor network theory and data analysis tools such as Laplacian eigenmaps and diffusion maps is discussed as well. Various algorithms for the numerical calculation of the various objects in TPT are also introduced. Finally, the theory and the algorithms are illustrated in several examples.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:43
Deposited By: Admin Administrator
Deposited On:03 Jan 2009 20:20
Last Modified:03 Mar 2017 14:39

Repository Staff Only: item control page