Math Physics Seminar, David Brydges, U of British Columbia, "The lace expansion for $\phi^{4}$"

Tue, Mar 29, 2016, 4:30 pm to 5:30 pm
Jadwin 343
The lace expansion provides a formula for the two point function which has been useful for critical percolation, self-avoiding walk and related problems in high dimensions. Recently Akira Sakai has shown that the Ising model and the one component $\phi^4$ model admit similar formulas. I will review the basic features of the lace expansion and describe recent work with Mark Holmes and Tyler Helmuth which extends the lace expansion to O(2) symmetric $\phi^4$.