Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761028
Title: Random interacting particle systems
Author: Gracar, Peter
ISNI:       0000 0004 7432 6935
Awarding Body: University of Bath
Current Institution: University of Bath
Date of Award: 2018
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Abstract:
Consider the graph induced by Z^d, equipped with uniformly elliptic random conductances on the edges. At time 0, place a Poisson point process of particles on Z^d and let them perform independent simple random walks with jump probabilities proportional to the conductances. It is well known that without conductances (i.e., all conductances equal to 1), an infection started from the origin and transmitted between particles that share a site spreads in all directions with positive speed. We show that a local mixing result holds for random conductance graphs and prove the existence of a special percolation structure called the Lipschitz surface. Using this structure, we show that in the setup of particles on a uniformly elliptic graph, an infection also spreads with positive speed in any direction. We prove the robustness of the framework by extending the result to infection with recovery, where we show positive speed and that the infection survives indefinitely with positive probability.
Supervisor: De Oliveira Stauffer, Alexandre ; Morters, Peter Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.761028  DOI: Not available
Keywords: Percolation ; Lipschitz ; Surface ; Multi-scale
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