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Universität Augsburg
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Universität Augsburg
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Professor Dr. Jack Hanson
City College of New York
spricht am
Freitag, 3. Mai 2024
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| In Bernoulli percolation, the incipient infinite cluster (IIC) is a version of the "open cluster of the origin at criticality conditioned to be infinite". Since this event should have probability 0 on $Z^d$, the IIC is constructed via a limiting procedure. For d > 6, several constructions have been given and shown to produce the same object, but many natural limiting procedures remain unexplored. For instance, it is an open question whether conditioning on {0 is connected to $\partial [-n, n]^d$} produces the IIC as $n \to \infty$. We answer this question in the affirmative as a corollary of our theorem, which roughly says "conditioning on any long open connection produces the IIC", and whose proof does not directly use lace expansion analysis. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Markus Heydenreich |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).