Yip, Siu Kwan (2014) On the Pfaffian property of annihilating random walk and coalescing random walk. PhD thesis, University of Warwick.

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Abstract

In this thesis we are to investigate two discrete interacting particle systems, namely annihilating random walk and coalescing random walk. By mapping the annihilating random walk to Glauber model and employing empty interval method respectively, we prove there is a similar structure behind them albeit their apparent differences, that is, they are both Pfaffian point process under a special initial condition.

Then we extend the result to investigate whether the Pfaffian property preserves in the case of multi-time correlation function, which is called extended Pfaffian property. And we also investigate the case which the initial condition is changed from independent particles to another peculiar one-sided initial condition and proved it also preserved the Pfaffian property.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Random walks (Mathematics), Pfaffian systems
Official Date:	May 2014
Dates:	Date Event May 2014 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Zaboronski, Oleg V. ; Tribe, Roger
Extent:	v, 114 leaves
Language:	eng

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