Critical phenomena in the Dyson hierarchical model and renormalization group

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Pavel Bleher This is my paper

classification math-phmath.MP

keywords criticaldysongrouphierarchicalmodelphenomenarenormalizationresults

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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
math.PR 2025-08 conditional novelty 8.0 of 10

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 long-range percolation I: High effective dimension
math.PR 2025-08 conditional novelty 8.0 of 10

In the regime d > min{6, 3alpha}, critical long-range percolation clusters have an n^{-1/2} volume tail and integrated superprocess scaling limits, switching from super-Levy (alpha < 2) to super-Brownian (alpha >= 2);...