Topics in stochastic processes with special reference to first passage percolation theory

Thesis

First passage percolation theory in its most general form is the randomised version of the well-known shortest route problem. It thus has several important physical applications. Ordinary percolation theory is but a special case of this more general problem which we formulate as follows.

To each arc of an arbitrary, countably infinite, connected graph we independently assign a non-negative random variable called the time coordinate of that arc. This assignment of random variables induces a time state 'w' on g. The 'length' of any path of g is the sum of the time coordinates of its component arcs.

[This abstract continues in the thesis file.]

Authors: Welsh, JAD

• DOI: 10.5287/ora-zb7yzdkx8
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English