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Markov chain algorithms for Eulerian orientations and 3-colourings of 2-dimensional Cartesian grids
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Johannes Fehrenbach
Veröffentlicht/Copyright:
25. September 2009
Abstract
In this paper we establish that the natural single point update Markov chain (also known as Glauber dynamics) for counting the number of Euler orientations of 2-dimensional Cartesian grids is rapidly mixing. This extends a result of Luby, Randall, and Sinclair (2001) who consider the case where orientations in the boundary are fixed. Similarly, we also obtain a rapid mixing result for the 3-colouring of rectangular Cartesian grids without fixing the boundaries. The proof uses path coupling and comparison to related Markov chains which allow additional transitions and which can be analysed directly.
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Published Online: 2009-09-25
Published in Print: 2004-02-01
© 2004 Oldenbourg Wissenschaftsverlag GmbH
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Artikel in diesem Heft
- Local maximin properties of tests in Gaussian shift experiments
- Markov chain algorithms for Eulerian orientations and 3-colourings of 2-dimensional Cartesian grids
- A two-dimensional Cramér–von Mises test for the two-sample problem with dispersion alternatives
- Necessary conditions for the existence of utility maximizing strategies under transaction costs
Artikel in diesem Heft
- Local maximin properties of tests in Gaussian shift experiments
- Markov chain algorithms for Eulerian orientations and 3-colourings of 2-dimensional Cartesian grids
- A two-dimensional Cramér–von Mises test for the two-sample problem with dispersion alternatives
- Necessary conditions for the existence of utility maximizing strategies under transaction costs
