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Loop percolation versus link percolation in the random loop model
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DOI：10.30757/ALEA.v23-20.png)
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Abstract
En 中文
In Mi lbacher (2021), Peter Mi hlbacher showed that in the random loop model without loop weights, a loop phase transition (assuming it exists) cannot occur at the same parameter as the percolation phase transition of the occupied edges. In this work, we give a quantitative version of this result, specifying a minimal gap between the percolation phase transition and a possible loop phase transition. A substantial part of our argument also works for weighted loop models.
Keywords:
Random loop model
blocking events
stochastic domination
Journal
A
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0.6
Papers:
24
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0