- AutorIn
- Deepan Basu
- Titel
- Generalizations and Interpretations of Incipient Infinite Cluster measure on Planar Lattices and Slabs
- Alternativtitel
- Verallgemeinerungen und Interpretationen vonIncipient-Infinite-Cluster-Maßen auf planaren Gittern und Platten
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-223724
- Datum der Einreichung
- 04.11.2016
- Datum der Verteidigung
- 08.03.2017
- Abstract (EN)
- This thesis generalizes and interprets Kesten\''s Incipient Infinite Cluster (IIC) measure in two ways. Firstly we generalize Járai\''s result which states that for planar lattices the local configurations around a typical point taken from crossing collection is described by IIC measure. We prove in Chapter 2 that for backbone, lowest crossing and set of pivotals, the same hold true with multiple armed IIC measures. We develop certain tools, namely Russo Seymour Welsh theorem and a strong variant of quasi-multiplicativity for critical percolation on 2-dimensional slabs in Chapters 3 and 4 respectively. This enables us to first show existence of IIC in Kesten\''s sense on slabs in Chapter 4 and prove that this measure can be interpreted as the local picture around a point of crossing collection in Chapter 5.
- Freie Schlagwörter (DE)
- Incipient-Infinite-Cluster-Maßen, Perkolation, Platten,
- Freie Schlagwörter (EN)
- Critical percolation, Planar percolation, Percolation on slabs, Incipient infinite cluster, IIC measure
- Klassifikation (DDC)
- 500
- GutachterIn
- Prof. Dr. Artem Sapozhnikov
- Prof. Dr. Markus Heydenreich
- BetreuerIn
- Prof. Dr. Artem Sapozhnikov
- Den akademischen Grad verleihende / prüfende Institution
- Universität Leipzig, Leipzig
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa-223724
- Veröffentlichungsdatum Qucosa
- 25.04.2017
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch