Random Walks, Disconnection and Random Interlacements David Windisch

ISBN: 9783838110493

Published: September 16th 2009

Paperback

172 pages


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Random Walks, Disconnection and Random Interlacements  by  David Windisch

Random Walks, Disconnection and Random Interlacements by David Windisch
September 16th 2009 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 172 pages | ISBN: 9783838110493 | 6.43 Mb

This work is about the disconnection of graphs by trajectories of random walks. Computer simulations show that the components left in a large graph after removing the trajectory of a simple random walk of a suitable timescale exhibit interestingMoreThis work is about the disconnection of graphs by trajectories of random walks. Computer simulations show that the components left in a large graph after removing the trajectory of a simple random walk of a suitable timescale exhibit interesting phase transitions, not unlike the ones encountered in the widely studied field of random graphs.

Disconnection phenomena of this kind are only beginning to be understood at a mathematically rigorous level. This thesis contributes to the field in several directions. The author studies the influence of a bias on the disconnection time of a discrete cylinder by a random walk, the vacant set left by a random walk on a discrete torus, and the link between random walk trajectories performing disconnection and the model of random interlacements, whereby questions on disconnection are related to problems in percolation theory.



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