Probability theory and related fields, 2020-04, Vol.176 (3-4), p.1011-1043
2020
Details
- Autor(en) / Beteiligte
- Titel
- A stationary planar random graph with singular stationary dual: dyadic lattice graphs
- Ist Teil von
- Probability theory and related fields, 2020-04, Vol.176 (3-4), p.1011-1043
- Ort / Verlag
- Berlin/Heidelberg: Springer Berlin Heidelberg
- Erscheinungsjahr
- 2020
- Link zum Volltext
- Quelle
- EBSCOhost Business Source Ultimate
- Beschreibungen/Notizen
- Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a singular stationary measure. This answers a question of Curien and shows behaviour different from the unimodular case. The consequence is that planar duality does not combine well with stationary random graphs. We also study harmonic measure on dyadic lattice graphs and show its singularity.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0178-8051eISSN: 1432-2064DOI: 10.1007/s00440-019-00934-0Titel-ID: cdi_proquest_journals_2252713659
- Format
- –
- Schlagworte
- Approximation, Economics, Finance, Graphs, Insurance, Management, Mathematical and Computational Biology, Mathematical and Computational Physics, Mathematics, Mathematics and Statistics, Operations Research/Decision Theory, Probability, Probability Theory and Stochastic Processes, Quantitative Finance, Random walk, Statistics for Business, Theoretical