Influence and sharp-threshold theorems for monotonic measures
Graham, B. T. ; Grimmett, G. R.
Ann. Probab., Tome 34 (2006) no. 1, p. 1726-1745 / Harvested from Project Euclid
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The influence theorem for product measures on the discrete space {0,1}N may be extended to probability measures with the property of monotonicity (which is equivalent to “strong positive association”). Corresponding results are valid for probability measures on the cube [0,1]N that are absolutely continuous with respect to Lebesgue measure. These results lead to a sharp-threshold theorem for measures of random-cluster type, and this may be applied to box crossings in the two-dimensional random-cluster model.
Publié le : 2006-09-14
Classification:  Influence,  sharp threshold,  monotonic measure,  FKG lattice condition,  positive association,  random-cluster model,  percolation,  60E15,  60K35,  82B31,  82B43 
@article{1163517221,
     author = {Graham, B. T. and Grimmett, G. R.},
     title = {Influence and sharp-threshold theorems for monotonic measures},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 1726-1745},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1163517221}
}

Graham, B. T.; Grimmett, G. R. Influence and sharp-threshold theorems for monotonic measures. Ann. Probab., Tome 34 (2006) no. 1, pp.  1726-1745. http://gdmltest.u-ga.fr/item/1163517221/