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Thursday, May 05, 2022
5:00 PM - 6:00 PM

LA Probability Forum

Plateaux estimates and their implications for percolation and self-avoiding walks in high-dimensions
Emmanuel Michta, Department of Mathematics, University of British Columbia,

UCLA, Math Sciences Room 6627

For torus percolation in high-dimensions the two-point function has a whole critical window (depending on the size of the torus) where it behaves more or less like the critical two-point function in Z^d. This fact can be summarized in a quantitative estimate called the plateau for the torus two-point function. A similar estimate conjecturally holds for the self-avoiding walk two-point function on a torus and partial results have been recently obtained in this direction. In this talk we will focus on plateaux estimates for those two models as well as on the various implications they have : ranging from the torus triangle condition in percolation to the asymptotic number of (weakly) self-avoiding walks on the torus. This is based on joint work with Tom Hutchcroft, Gordon Slade and Jiwoon Park.

For more information, please contact Math Dept by phone at 626-395-4335 or by email at mathinfo@caltech.edu.