In the long-range low-dimensional regime of percolation, the cluster volume tail and k-point functions are determined up to constants, yielding the hyperscaling identities delta=(d+alpha)/(d-alpha) and d_f=(d+alpha)/2.
Critical phenomena in the Dyson hierarchical model and renormalization group
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We review some results on the critical phenomena in the Dyson hierarchical model and renormalization group.
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Critical long-range percolation II: Low effective dimension
In the long-range low-dimensional regime of percolation, the cluster volume tail and k-point functions are determined up to constants, yielding the hyperscaling identities delta=(d+alpha)/(d-alpha) and d_f=(d+alpha)/2.