Recurrence of bipartite planar maps
2014 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 19, 31- p.Article in journal (Refereed) Published
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).
Place, publisher, year, edition, pages
2014. Vol. 19, 31- p.
Planar maps, local limits, simply generated trees, random walk
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-232666DOI: 10.1214/EJP.v19-3102ISI: 000340998000001OAI: oai:DiVA.org:uu-232666DiVA: diva2:749021