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15 Aug 2012: They play important roles in matroid theory, [20],computational complexity, [22, 23, 24], and models of statistical physics,[21, 24]. ... 20] D. J. A. Welsh. Matroid Theory. Academic Press, London, 1976.

15 Aug 2012: The almost-sure uniqueness of the infinite entanglement has been explored in [20, 29], andthe situation is similar to that for rigidity percolation. ... See [20]. 5. The random-cluster model. The random-cluster model on a finite graph G = (V, E) is a

15 Aug 2012: Therst-passage problem and the time constant (p;q) have been studied in detail when q = 1;see [19, 20]. ... Advances inApplied Probability 12, 848{863.20. Kesten, H. (1986). Aspects of rst-passage percolation.

7 Feb 2012: Seminar at Microsoft, Cambridge, June 20, 2011. The Multi-armed Bandit Problem.

15 Aug 2012: Itremains to prove (2.20), and we shall use monotonicity again for this. ... INFLUENCE FOR MONOTONIC MEASURES 23. [20] Russo, L. (1982). An approximate zero–one law.

15 Aug 2012: We illustrate this approach in the nextsection, by sketching the details in a particular case.Important references include [20, 157, 158, 269]. ... The following theorem is taken from [20] and may be proved in amanner similar to the proof given in the

15 Aug 2012: POTTS MODELS AND RANDOM-CLUSTER. PROCESSES WITH MANY-BODY INTERACTIONS. Geoffrey GrimmettAbstra t. Known differential inequalities for certain ferromagnetic Potts models with pair-interactions may be extended to Potts models with many-body

15 Aug 2012: This is not the first general account of the area. Much of the basic methodologywas published first in the remarkable series of papers of Fortuin and Kasteleyn [18,19, 20, 21, ... The percolation model, Physica 58,. 393–418. 20. Fortuin, C. M. (1972b),

15 Aug 2012: October 1996. Note added at reprinting. GRG thanks Roberto Schonmann for pointing outan error in the proof of equation (8.20), corrected in this reprint.

21 Mar 2012: Lemma 5.5 gives F(x) = F(x). 20. 6 Bandit Processes and the Gittins Index.