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Percolation on fitness landscapes: Effects of correlation, phenotype, and incompatibilities
, 2007
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Is the fuzzy Potts model Gibbsian?
, 2002
"... The fuzzy Potts model is obtained by looking at the Potts model with a pair of glasses that prevents distinguishing between some of the spin values. We show that the fuzzy Potts model on Z (d 2) is Gibbsian at high temeratures and nonGibbsian at low temperatures. ..."
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Cited by 9 (1 self)
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The fuzzy Potts model is obtained by looking at the Potts model with a pair of glasses that prevents distinguishing between some of the spin values. We show that the fuzzy Potts model on Z (d 2) is Gibbsian at high temeratures and nonGibbsian at low temperatures.
Limit Theorems for the Painting of Graphs By Clusters
 ESAIM PROBAB. STATIST
, 2001
"... We consider a generalization of the socalled divide and color model recently introduced by Häggström . We investigate the behaviour of the magnetization in large boxes and its fluctuations. Thus, laws of large numbers and Central Limit theorems are proved, both quenched and annealed. We show that t ..."
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Cited by 4 (2 self)
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We consider a generalization of the socalled divide and color model recently introduced by Häggström . We investigate the behaviour of the magnetization in large boxes and its fluctuations. Thus, laws of large numbers and Central Limit theorems are proved, both quenched and annealed. We show that the properties of the underlying percolation process roughly influence the behaviour of the colorying model. In the subcritical case, the limit magnetization is deterministic and the Central Limit Theorem admits a Gaussian limit. A contrario, the limit magnetization is not deterministic in the supercritical case and the limit of the Central Limit Theorem is not Gaussian, except in the particular model with exactly two colors which are equally probable.
Percolation Phenomena in Low and High Density Systems
"... that in the translation invariant measure, averaged over the disorder, at self–dual points any amalgamation of q − 1 species will fail to percolate despite an overall (high) density of 1 − q −1. Further, in the dilute bond version of these systems, if the system is just above threshold, then through ..."
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Cited by 4 (1 self)
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that in the translation invariant measure, averaged over the disorder, at self–dual points any amalgamation of q − 1 species will fail to percolate despite an overall (high) density of 1 − q −1. Further, in the dilute bond version of these systems, if the system is just above threshold, then throughout the low temperature phase there is percolation of a single species despite a correspondingly small density. Finally, we demonstrate both phenomena in a single model by considering a “perturbation ” of the dilute model that has a self–dual point. We also demonstrate that these phenomena occur, by a similar mechanism, in a simple coloring model invented by O. Häggström.
Renormalization Group, NonGibbsian states, their relationship and further developments
, 2005
"... We review what we have learned about the “Renormalization Group peculiarities ” which were discovered more than twentyfive years ago by Griffiths and Pearce. We discuss which of the questions they asked have been answered and which ones are still widely open. The problems they raised have led to the ..."
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We review what we have learned about the “Renormalization Group peculiarities ” which were discovered more than twentyfive years ago by Griffiths and Pearce. We discuss which of the questions they asked have been answered and which ones are still widely open. The problems they raised have led to the study of nonGibbsian states (probability measures). We also mention some further related developments, which find applications in nonequilibrium questions and disordered models.