AG Mathematische Physik, Claus Köstler (Cork): Distributional symmetries and invariance principles in noncommutative probability

Claus Köstler (Cork)

Distributional symmetries and invariance principles in noncommutative
probability

Abstract: Distributional symmetries and invariance principles provide deep
structural results in classical probability. For example, the de Finetti
theorem characterizes an infinite sequence of random variables to be conditional
independent and identically distributed if and only if its joint distribution is
invariant under permuting these random variables. Recently significant progress
was made in transferring such de Finetti type results to an operator algebraic
setting of noncommutative probability. My talk will introduce to and overview
some of these newer developments.

Selected References:
[1] Köstler, Claus. A noncommutative extended de Finetti theorem. J. Funct.
Anal. 258 (2010), no. 4, 1073–1120.
[2] Gohm, Rolf; Köstler, Claus. Noncommutative independence from the braid group
B∞. Comm. Math. Phys. 289 (2009), no. 2, 435–482.
[3] Köstler, Claus; Speicher, Roland. A noncommutative de Finetti theorem:
invariance under quantum permutations is equivalent to freeness with
amalgamation. Comm. Math. Phys. 291 (2009), no. 2, 473–490.
[4] Dykema, Kenneth J.; Köstler, Claus; Williams, John D. Quantum symmetric
states on free product C∗-algebras. Trans. Amer. Math. Soc. 369 (2017), no. 1,
645–679.
[5] Evans, D. Gwion; Gohm, Rolf; Köstler, Claus. Semi-cosimplicial objects and
spreadability. Rocky Mountain J. Math. 47 (2017), no. 6, 1839–1873.
[6] Köstler, Claus; Krishnan, Arundhathi; Wills, Stephen J. Markovianity and the
Thompson Monoid F+. ePrint arXiv:2009.14811, to appear in J. Funct. Anal.
[7] Köstler, Claus; Krishnan, Arundhathi. Markovianity and the Thompson Group F.
SIGMA Symmetry Integrability Geom. Methods Appl. 18 (2022), Paper No. 083.