Macroscopic loops exist in the random loop model on sparse random graphs above an explicit edge density threshold depending on loop weight θ and cross parameter u.
Existence of a phase transition of the interchange process on the Hamming graph.Electronic Journal of Probability, 24:1–21
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Macroscopic loops in the random loop model on sparse random graphs
Macroscopic loops exist in the random loop model on sparse random graphs above an explicit edge density threshold depending on loop weight θ and cross parameter u.