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  1. Article

    Open Access

    Loewner Theory for Bernstein Functions I: Evolution Families and Differential Equations

    One-parameter semigroups of holomorphic functions appear naturally in various applications of Complex Analysis, and in particular, in the theory of (temporally) homogeneous branching processes. A suitable anal...

    Pavel Gumenyuk, Takahiro Hasebe, José-Luis Pérez in Constructive Approximation (2024)

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  2. No Access

    Article

    Bi-monotonic Independence for Pairs of Algebras

    In this article, the notion of bi-monotonic independence is introduced as an extension of monotonic independence to the two-faced framework for a family of pairs of algebras in a non-commutative space. The ass...

    Yinzheng Gu, Takahiro Hasebe, Paul Skoufranis in Journal of Theoretical Probability (2020)

  3. Article

    Open Access

    On Free Generalized Inverse Gaussian Distributions

    We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the classical GIG distribution. In par...

    Takahiro Hasebe, Kamil Szpojankowski in Complex Analysis and Operator Theory (2019)

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    Article

    Limit theorems in bi-free probability theory

    In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of self-adjoint commuting random variables in an infinites...

    Takahiro Hasebe, Hao-Wei Huang, Jiun-Chau Wang in Probability Theory and Related Fields (2018)

  5. No Access

    Article

    Order quasisymmetric functions distinguish rooted trees

    Richard P. Stanley conjectured that finite trees can be distinguished by their chromatic symmetric functions. In this paper, we prove an analogous statement for posets: Finite rooted trees can be distinguished...

    Takahiro Hasebe, Shuhei Tsujie in Journal of Algebraic Combinatorics (2017)

  6. No Access

    Article

    Unimodality of the Freely Selfdecomposable Probability Laws

    We show that any freely selfdecomposable probability law is unimodal. This is the free probabilistic analog of Yamazato’s result in (Ann. Probab. 6:523–531, 1978).

    Takahiro Hasebe, Steen Thorbjørnsen in Journal of Theoretical Probability (2016)

  7. No Access

    Article

    Free Subordination and Belinschi–Nica Semigroup

    We realize the Belinschi–Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with respect to free multiplicative c...

    Octavio Arizmendi, Takahiro Hasebe in Complex Analysis and Operator Theory (2016)

  8. No Access

    Article

    Conditionally Monotone Independence II: Multiplicative Convolutions and Infinite Divisibility

    We study the multiplicative convolution for c-monotone independence. This convolution unifies the monotone, Boolean and orthogonal multiplicative convolutions. We characterize convolution semigroups for the c-...

    Takahiro Hasebe in Complex Analysis and Operator Theory (2013)

  9. No Access

    Article

    Analytic Continuations of Fourier and Stieltjes Transforms and Generalized Moments of Probability Measures

    We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the...

    Takahiro Hasebe in Journal of Theoretical Probability (2012)