Diagrammatic bounds on the lace-expansion coefficients for oriented percolation

Abstract

We provide a complete proof of the diagrammatic bounds on the lace-expansion coefficients for oriented percolation, which are used in [arXiv:math/0703455] to investigate critical behavior for long-range oriented percolation above 2\min{α,2} spatial dimensions.

11 pages, supporting manuscript for [arXiv:math/0703455]

Cited by in corpus (3)

• Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation
• Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation
• Mean-field behavior of nearest-neighbor oriented percolation on the BCC lattice above $8+1$ dimensions