Bootstrap Analysis of the Lace Expansion

Abstract

We complete the proof of the infrared bound. For this, we analyze the lace-expansion recurrence relation in Fourier space, and reduce its asymptotics to necessary bounds on the lace-expansion coefficients that have been obtained in the previous chapter. Finally, we summarize some consequences of the completed bootstrap argument that are interesting in their own right, such as asymptotics of the critical threshold in high dimensions.