Lace expansion for dummies

Erwin Bolthausen; Remco Van Der Hofstad; Gady Kozma

doi:10.1214/16-AIHP797

Lace expansion for dummies

Erwin Bolthausen, Remco Van Der Hofstad, Gady Kozma

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

We show Green's function asymptotic upper bound for the two-point function of weakly self-Avoiding walk in d >4, revisiting a classic problem. Our proof relies on Banach algebras to analyse the lace-expansion fixed point equation and is simpler than previous approaches in that it avoids Fourier transforms.

Original language	English
Pages (from-to)	141-153
Number of pages	13
Journal	Annales de l'institut Henri Poincare (B): Probability and Statistics
Volume	54
Issue number	1
DOIs	https://doi.org/10.1214/16-AIHP797
Publication status	Published - 1 Feb 2018

Funding

Supported by SNF Grant 200020-138141. 2Supported by the Netherlands Organisation for Scientific Research (NWO) through VICI Grant 639.033.806 and the Gravitation NETWORKS Grant 024.002.003.

Keywords

Banach algebra
Deconvolution
Edgeworth expansion
Lace expansion
Self-Avoiding walk

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10.1214/16-AIHP797

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Lace expansion for dummies

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