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2014 Recurrence of bipartite planar maps
Jakob Björnberg, Sigurdur Stefánsson
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Electron. J. Probab. 19: 1-40 (2014). DOI: 10.1214/EJP.v19-3102


This paper concerns random bipartite planar maps which are defined by assigning weights to their faces. The paper presents a threefold contribution to the theory. Firstly, we prove the existence of the local limit for all choices of weights and describe it in terms of an infinite mobile. Secondly, we show that the local limit is in all cases almost surely recurrent. And thirdly, we show that for certain choices of weights the local limit has exactly one face of infinite degree and has in that case spectral dimension 4/3 (the latter requires a mild moment condition).


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Jakob Björnberg. Sigurdur Stefánsson. "Recurrence of bipartite planar maps." Electron. J. Probab. 19 1 - 40, 2014.


Accepted: 12 March 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1286.05153
MathSciNet: MR3183575
Digital Object Identifier: 10.1214/EJP.v19-3102

Primary: 05C80
Secondary: 05C05 , 05C81 , 60F05 , 60J80

Keywords: Local limits , planar maps , Random walk , Simply generated trees


Vol.19 • 2014
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