Universality conjecture for random-cluster divide-and-colour scaling limits
Universality conjecture for random-cluster divide-and-colour scaling limits
Let be the divide-and-colour model associated with a random-cluster measure with parameters and , and consider it on the triangular lattice at . Universality conjecture. For every and every , the site-percolation scaling limit of
is the same as the scaling limit of critical Bernoulli site percolation. This conjecture expresses the expectation that short-range correlations below the random-cluster critical point do not change the critical scaling limit; the source does not state a resolution.
Sources & referencesView supporting material
Primary source
Andras Balint, Federico Camia and Ronald Meester, “Sharp phase transition and critical behaviour in 2D divide and colour models”, arXiv:0708.3349 (2007).
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