Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Lace expansion for dummies

Erwin Bolthausen, Remco van der Hofstad, and Gady Kozma

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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.


Nous montrons une domination asymptotique de la fonction à deux points de la marche faiblement auto-évitante en dimension $d>4$ par la fonction de Green, revisitant ainsi un problème classique. Notre preuve s’appuie sur des techniques d’algèbres de Banach pour analyser le point fixe de l’équation de développement en lacets. Elle est plus simple que les approches précédentes car elle ne passe pas par la transformée de Fourier.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 1 (2018), 141-153.

Received: 26 April 2016
Revised: 27 August 2016
Accepted: 22 September 2016
First available in Project Euclid: 19 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 84B41 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Self-avoiding walk Lace expansion Banach algebra Deconvolution Edgeworth expansion


Bolthausen, Erwin; van der Hofstad, Remco; Kozma, Gady. Lace expansion for dummies. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 1, 141--153. doi:10.1214/16-AIHP797.

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