UBC Probability Seminar: Gordon Slade

We apply and extend the renormalisation group method developed by Bauerschmidt, Brydges and Slade to analyse near-critical finite-size scaling for the 4-dimensional n-component hierarchical |ϕ|⁴ model, for all n=1,2,3,… In particular, we compute the universal scaling profile of the susceptibility in a critical window around the infinite-volume critical point. Our methods have the potential to extend from the hierarchical to the Euclidean model. Implications for the self-avoiding walk (the case n=0) are also discussed.

This is based on joint work in progress with Emmanuel Michta and Jiwoon Park.