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DTSTART:20210328T030000
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DTSTAMP:20230327T170456Z
UID:1615303800@ist.ac.at
DTSTART:20210309T163000
DTEND:20210309T171500
DESCRIPTION:Speaker: Ioan Manolescu\nhosted by M. Beiglböck\, N. Berestyck
i\, L. Erdös\, J. Maas\, F. Toninelli\nAbstract: We prove the asymptotic
rotational invariance of the critical FK-percolation model on the square l
attice with any cluster-weight between 1 and 4. These models are expected
to exhibit conformally invariant scaling limits that depend on the cluster
weight\, thus covering a continuum of universality classes. The rotation
invariance of the scaling limit is a strong indication of the wider confor
mal invariance\, and may indeed serve as a stepping stone to the latter.Ou
r result is obtained via a universality theorem for FK-percolation on cert
ain isoradial lattices. This in turn is proved via the star-triangle (or Y
ang-Baxter) transformation\, which may be used to gradually change the squ
are lattice into any of these isoradial lattices\, while preserving certai
n features of the model. It was previously proved that throughout this tra
nsformation\, the large scale geometry of the model is distorted by at mos
t a limited amount. In the present work we argue that the distortion becom
es insignificant as the scale increases. This hinges on the interplay bet
ween the inhomogeneity of isoradial models and their embeddings\, which co
mpensate each other at large scales. As a byproduct\, we obtain the asympt
otic rotational invariance also for models related to FK-percolation\, suc
h as the Potts and six-vertex ones. Moreover\, the approach described here
is fairly generic and may be adapted to other systems which possess a Yan
g-Baxter transformation. Based on joint work with Hugo Duminil-Copin\, K
arol Kajetan Kozlowski\, Dmitry Krachun and Mendes Oulamara.
LOCATION:Online via Zoom\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Ioan Manolescu: Rotational invariance of the critical planar FK-per
colation model
URL:https://talks-calendar.ista.ac.at/events/3120
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