Abstract
We prove bounds on the lace-expansion coefficients \(\varPi ^{(\mathrm {N})}\) identified in the previous chapter. These bounds are an essential ingredient in the lace-expansion proof of the infrared bound. We refer to the methods of this section as diagrammatic estimates, as we use Feynman diagrams to provide a convenient representation for upper bounds on \(\varPi ^{(\mathrm {N})}\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Heydenreich, M., van der Hofstad, R. (2017). Diagrammatic Estimates for the Lace Expansion. In: Progress in High-Dimensional Percolation and Random Graphs. CRM Short Courses. Springer, Cham. https://doi.org/10.1007/978-3-319-62473-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-62473-0_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62472-3
Online ISBN: 978-3-319-62473-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)