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Coalescing random walks and universality in two dimensions
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Lukins, Jamie (2020) Coalescing random walks and universality in two dimensions. PhD thesis, University of Warwick.
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WRAP_Theses_Lukins_2020.pdf - Submitted Version - Requires a PDF viewer. Download (1214Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3518275~S15
Abstract
We study infinite systems of coalescing nearest neighbour random walks on the integer lattice, Z 2 . We are interested in the decay of the probability that the origin is occupied as time increases. This is a well known result for the case that the random walks coalesce instantaneuously and was first proved by Bramson and Griffeath in [2]. We rederive this result and strengthen it by providing an error bound by using the methods employed by van den Berg and Kesten in [27], where they worked in dimensions greater than 2. We further study coalescing random walks that do not coalesce immediately on collision, but can occupy the same site for an exponential (rate λ ∈ (0, ∞)) random time before coalescing, in this was they have a chance to walk away before coalescing. We derive the analogous asymptotic for the decay of the probability of the occupation of the origin and find that, in two dimensions, this decay is independent of the coalescence rate λ in the leading order and agrees with the decay for the instantaneuously coalescing walks.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Random walks (Mathematics) | ||||
Official Date: | October 2020 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Tribe, Roger ; Zaboronski, Oleg V. | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Format of File: | |||||
Extent: | vii, 190 leaves : illustrations | ||||
Language: | eng |
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