How many T‐tessellations on k lines? Existence of associated Gibbs measures on bounded convex domains. Issue 3 (2nd July 2014)

• Record Type: Journal Article
• Authors: Kahn, Jonas
• Is Part Of: Random structures & algorithms. Volume 47:Issue 3(2015)
• Page Start: 561
• Page End: 587
• Publication Date: 2014-07-02
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20557
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>The paper bounds the number of tessellations with T‐shaped vertices on a fixed set of <italic>k</italic> lines: tessellations are efficiently encoded, and algorithms retrieve them, proving injectivity. This yields existence of a completely random T‐tessellation, as defined by Kiêu et al. (Spat Stat 6 (2013) 118–138), and of its Gibbsian modifications. The combinatorial bound is sharp, but likely pessimistic in typical cases. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 561–587, 2015</p> </abstract>