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Title: Slowly-coalescing Brownian motion
Author: Hobson, Tim
ISNI:       0000 0001 3579 5710
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2007
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An interacting particle system is constructed in which a collection of independent Brownian motions are subject to the rule that each pair of particles shall coalesce at a rate given formally by ). dLt , where {Lt : t ~ O} is the intersection local time of the pair. This interaction mechanism is referred to as slowly-coalescing, in contrast to the more standard model in which particles coalesce immediately on collision. The process is shown to be the weak limit of a sequence of coalescing symmeteric random walks on the lattice n-1Z. Our indirect argument exploits the existence of a dual Markov process at both the discrete and the continuous level. By endowing each of the slowly-coalescing Brownian particles with a weight we are able to establish a more intimate duality, the dual process being the solution of a stochastic heat equation driven by Fisher-Wright noise.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available