Uniform infinite planar quadrangulations with a boundary. Issue 1 (11th March 2014)

• Record Type: Journal Article
• Authors: Curien, Nicolas; Miermont, Grégory
• Is Part Of: Random structures & algorithms. Volume 47:Issue 1(2015)
• Page Start: 30
• Page End: 58
• Publication Date: 2014-03-11
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20531
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>We introduce and study the uniform infinite planar quadrangulation (UIPQ) with a boundary via an extension of the construction of Curien et al. (Curien et al., Lat Am J Probab Math Stat 49 (2013) 340–373). We then relate this object to its simple boundary analog using a pruning procedure. This enables us to study the aperture of these maps, that is, the maximal graph distance between two points on the boundary, which in turn sheds new light on the geometry of the UIPQ. In particular we prove that the self‐avoiding walk on the UIPQ is at most diffusive. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 30–58, 2015</p> </abstract>