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Title of Journal: Math Z

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Abbravation: Mathematische Zeitschrift

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Springer-Verlag

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DOI

10.1007/978-3-319-12352-3_20

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1432-1823

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Cumulants in noncommutative probability theory I

Authors: Franz Lehner
Publish Date: 2004/04/09
Volume: 248, Issue: 1, Pages: 67-100
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Abstract

Cumulants linearize convolution of measures We use a formula of Good to define noncommutative cumulants in a very general setting It turns out that the essential property needed is exchangeability of random variables Roughly speaking the formula says that cumulants are moments of a certain ‘‘discrete Fourier transform’’ of a random variable This provides a simple unified method to understand the known examples of cumulants like classical free and various qcumulants

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Other Papers In This Journal:
  1. On profinite groups in which commutators are covered by finitely many subgroups
  2. Stable reduction of curves and tame ramification
  3. Constant mean curvature graphs on exterior domains of the hyperbolic plane
  4. On weighted critical imbeddings of Sobolev spaces
  5. Mixed Hessian inequalities and uniqueness in the class $$\mathcal {E}(X,\omega ,m)$$
  6. Generalized Liouville differentiation, truncated hypersingular integrals and K -functionals
  7. Polynomial inequalities and universal Taylor series
  8. Computations of the orbifold Yamabe invariant
  9. Grušin operators, Riesz transforms and nilpotent Lie groups
  10. Real K 3 surfaces without real points, equivariant determinant of the Laplacian, and the Borcherds Φ-function
  11. Positive semidefinite diagonal minus tail forms are sums of squares
  12. On the measures of large entropy on a positive closed current
  13. Fano varieties in index one Fano complete intersections
  14. Families over special base manifolds and a conjecture of Campana
  15. On the holomorphic structure of G -orbits in compact hermitian symmetric spaces
  16. Derivations, the Lawrence–Sullivan interval and the Fiorenza–Manetti mapping cone
  17. On the geometry of model almost complex manifolds with boundary
  18. The eta invariant in the doubly Kählerian conformally compact Einstein case
  19. Injectivity radius and diameter of the manifolds of flags in the projective planes
  20. On the invariant distributions of $$C^2$$ circle diffeomorphisms of irrational rotation number
  21. On Hörmander’s solution of the $$\bar{\partial }$$-equation. I
  22. Capillary surfaces in a convex cone
  23. Harmonic maps of finite uniton number into G 2
  24. On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms
  25. On irregular binomial D -modules
  26. Self-similar solutions for the Schrödinger map equation
  27. Harmonicity of sections of sphere bundles
  28. Cluster categories of type $${\mathbb {A}}_\infty ^\infty $$ and triangulations of the infinite strip
  29. A lower bound on Seshadri constants of hyperplane bundles on threefolds
  30. Saturated fusion systems over $$\mathcal {A}_2$$-groups
  31. Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature
  32. On newforms for Kohnen plus spaces
  33. Finiteness of the basic intersection cohomology of a Killing foliation
  34. Distributional chaos for operators with full scrambled sets
  35. Packing dimension and Ahlfors regularity of porous sets in metric spaces
  36. Invariance de la Γ-dimension pour certaines familles kählériennes de dimension 3
  37. Effective formulas for the local Łojasiewicz exponent
  38. Stein structures and holomorphic mappings
  39. Actions of arithmetic groups on homology spheres and acyclic homology manifolds
  40. Divergence form operators in Reifenberg flat domains
  41. Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups
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