Corpus ID: 221340685

Density of imaginary multiplicative chaos via Malliavin calculus

@inproceedings{Aru2020DensityOI,
  title={Density of imaginary multiplicative chaos via Malliavin calculus},
  author={Juhan Aru and Antoine Jego and Janne Junnila},
  year={2020}
}
  • Juhan Aru, Antoine Jego, Janne Junnila
  • Published 2020
  • Mathematics, Physics
  • We consider the imaginary Gaussian multiplicative chaos, i.e. the complex Wick exponential μβ :=: e iβΓ(x) : for a log-correlated Gaussian field Γ in d ≥ 1 dimensions. We show that for any nonzero and bounded test function f , the complex-valued random variable μβ(f) has a smooth density w.r.t. the Lebesgue measure on C. Our main tool is Malliavin calculus, which seems to be well-adapted to the study of (complex) multiplicative chaos. To apply Malliavin calculus to imaginary chaos, we develop… CONTINUE READING

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 17 REFERENCES
    Complex Gaussian Multiplicative Chaos
    • 50
    • PDF
    Gaussian multiplicative chaos revisited
    • 125
    • PDF
    Reconstructing the base field from imaginary multiplicative chaos
    • 1
    • PDF
    Integrability of Liouville theory: proof of the DOZZ Formula
    • 47
    • PDF
    The Fyodorov-Bouchaud formula and Liouville conformal field theory
    • 33
    • PDF
    Decompositions of log-correlated fields with applications
    • 16
    • PDF
    A PROBABILISTIC APPROACH OF ULTRAVIOLET RENORMALISATION IN THE BOUNDARY SINE-GORDON MODEL
    • 12
    • PDF
    Dimension of two-valued sets via imaginary chaos.
    • 4
    • Highly Influential
    • PDF
    The Malliavin Calculus and Related Topics
    • 2,920
    • Highly Influential