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math.PR2023
Percolation on hypergraphs and the hard-core model
Tyler Helmuth, Will Perkins, Michail Sarantis
We prove tight bounds on the site percolation threshold for -uniform hypergraphs of maximum degree and for -uniform hypergraphs of maximum degree in which any pair of…
math.PR2023
Directed Spatial Permutations on Asymmetric Tori
Alan Hammond, Tyler Helmuth
We investigate a model of random spatial permutations on two-dimensional tori, and establish that the joint distribution of large cycles is asymptotically given by the Poisson--Dir…