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DTSTAMP:20230327T162007Z
UID:1636038900@ist.ac.at
DTSTART:20211104T161500
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DESCRIPTION:Speaker: Haonan Zhang\nhosted by Laszlo Erdös\nAbstract: In a
celebrated paper in 1973\, Lieb proved what we now call Lieb's Concavity T
heorem and resolved a conjecture of Wigner-Yanase-Dyson. In this talk\, I
will present a very simple variational method to study the concavity/conve
xity of trace functionals. This allows us to reduce many concavity/convexi
ty problems to certain fundamental results: mainly this 1973 concavity the
orem of Lieb and its complementary convexity result of Ando in 1979. Along
the way\, we settle a conjecture of Carlen-Frank-Lieb concerning "double
convexity". A weaker form of this conjecture was made earlier by Audenaert
-Datta when studying the data processing inequalities for alpha-z Rényi r
elative entropies. We also prove "triple convexity" theorems\, which exten
d some results of Hiai-Petz and Carlen-Frank-Lieb. Such "triple convexity"
results are related to a conjecture by Al-Rashed and Zegarlinski\, which
we will prove using complex interpolation. Moreover\, this variational met
hod is also helpful in proving non-concavity/non-convexity results. One ca
n use this to disprove a strategy of Chehade proposed to study equality co
nditions of data processing inequalities. The talk is based on arXiv:1811
.01205 and arXiv:2108.05785.
LOCATION:Mondi 2 (I01.01.008)\, Central Building\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Haonan Zhang: A variational method and its applications in concavit
y/convexity of trace functionals
URL:https://talks-calendar.ista.ac.at/events/3394
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