Séminaire de Mathématique

Scaling in Percolation Models with Long-Range Correlations

by Pierre-François Rodriguez (Imperial College London)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Probability and analysis informal seminar

The talk will present recent progress towards a rigorous understanding of the critical regime associated to continuous phase transitions in the presence of long-range correlations, in dimensions larger than 2. Our findings deal with a 3-dimensional percolation model built from the harmonic crystal, which benefits from a rich interplay with potential theory for the associated diffusion. The results rigorously exhibit the scaling behavior of various observables of interest and unveil the values of the associated critical exponents, which are consistent with scaling theory below the upper-critical dimension (expectedly equal to 6). This confirms various predictions by physicists based on non-rigorous renormalization group techniques, notably that of Weinrib-Halperin concerning the value of the associated correlation length exponent. It also yields a proof of Fisher’s scaling relation for this model. Based on joint works with Alex Drewitz and Alexis Prevost.



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Organized by

Thierry Bodineau, Pieter Lammers, Yilin Wang