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SUMMARY:Total Positivity in Planar Spin Systems
DTSTART;VALUE=DATE-TIME:20170913T143000Z
DTEND;VALUE=DATE-TIME:20170913T153000Z
DTSTAMP;VALUE=DATE-TIME:20200716T050214Z
UID:indico-event-2547@indico.math.cnrs.fr
DESCRIPTION:Totally positive matrices are characterized by having all thei
r minors positive. They appear in various areas of physics and mathematics
\, including oscillations in mechanical systems\, quantum groups\, and alg
ebraic geometry. It has been known since the work of Fomin that the two-po
int correlations functions of the two-dimensional Gaussian free field sati
sfy total positivity. I will present an analogous result for the correlati
ons of the planar Ising model. The idea is to prove that determinants of s
uch correlations have interpretations in terms of probabilities of events
in the random current model. A natural open question is to identify all pl
anar totally positive spin systems.\n\nhttps://indico.math.cnrs.fr/event/2
547/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2547/
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