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Torus plateaux in high-dimensional critical phenomena

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SSDW01 - Self-interacting processes

Boundary conditions play an important role in the finite-size scaling of critical statistical mechanical models in high dimensions.  For periodic boundary conditions, the critical two-point function decays at small distances like the infinite-volume two-point function, but at larger distances it levels off to a constant “plateau” value.  This phenomenon has been proved for self-avoiding walk and spin systems in dimensions d>4 and for percolation in dimensions d>6.  Results for a hierarchical spin model lead, via a universality hypothesis, to striking conjectures for universal scaling profiles and non-Gaussian limits.  This talk will give a survey of recent collaborations with Tom Hutchcroft, Yucheng Liu, Emmanuel Michta, Romain Panis, and Jiwoon Park.

This talk is part of the Isaac Newton Institute Seminar Series series.

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