Research interest

• Free probability (Aspects of complex analysis and combinatorics, in particular)

Muraki's preprint

Preprints

1. O. Arizmendi, T. Hasebe, Y. Kitagawa, Free multiplicative convolution with an arbitrary measure on the real line. arXiv:2503.14992
2. T. Hasebe, J. Masamune, T. Oka, K. Sakai, T. Yamada, Construction of signed distance functions with an elliptic equation. arXiv:2401.17665
3. B. Collins, K. Fujie, T. Hasebe, F. Leid and N. Sakuma, Fluctuations of eigenvalues of a polynomial on Haar unitary and finite rank matrices. arXiv:2309.15396
4. T. Hasebe, I. Hotta and T. Murayama, Notes on locally uniform weak convergence with application to additive processes. arXiv:2301.04361
5. P. Gumenyuk, T. Hasebe and J.-L. Pérez, Loewner Theory for Bernstein functions II: applications to inhomogeneous continuous-state branching processes. arXiv:2211.12442
6. T. Hasebe, A three-state independence in non-commutative probability. arXiv:1009.1505   (A thorough revision of the older version "New associative product of three states generalizing free, monotone, anti-monotone, Boolean, conditionally free and conditionally monotone products".)

List of Publication

Free probability, noncommutative probability

1. K. Fujie and T. Hasebe, Free probability of type B prime. Accepted for publication from Trans. Amer. Math. Soc. arXiv:2310.14582
2. T. Hasebe and H.-W. Huang, Limit theorems and wrapping transforms in bi-free probability theory, Pacific J. Math. 329 (2024), No. 1, 63-104. arXiv:2007.02775
3. T. Hasebe, K. Noba, N. Sakuma and Y. Ueda, On Boolean selfdecomposable distributions. Studia Math. 274 (2024), No. 2, 129-151. Online first version   arXiv:2206.04932
4. O. Arizmendi, T. Hasebe and F. Lehner, Cyclic independence: Boolean and monotone, Algebr. Combin. 6 (2023), no. 6, 1697-1734. https://doi.org/10.5802/alco.309  (open access)  arXiv:2204.00072
5. T. Hasebe and Y. Ueda, On the free Lévy measure of the normal distribution. Electron. J. Probab. 28 (2023), 1-19. https://doi.org/10.1214/23-EJP1035  (open access)
6. T. Hasebe and F. Lehner, Cumulants, Spreadability and the Campbell-Baker-Hausdorff Series. Doc. Math. 28 (2023), no. 3, 515-601. https://doi.org/10.4171/DM/923  (open access)  arXiv:1711.00219
7. M. Gerhold, T. Hasebe and M. Ulrich, Towards a Classification of Multi-Faced Independence: A Representation-Theoretic Approach, J. Funct. Anal. 285, Issue 3 (2023), 109907. arXiv:2111.07649
8. T. Hasebe, Y. Ueda and J.-C. Wang, Log-unimodality for free positive multiplicative Brownian motion, Colloq. Math. 169 (2022), 209-226. arXiv:2009.13848
9. T. Hasebe and I. Hotta, Additive processes on the unit circle and Loewner chains, Int. Math. Res. Not. 2022, Issue 22, November 2022, 17797–17848. arXiv:2010.15194
10. M. Fukuda, T. Hasebe and S. Sato, Additivity violation of quantum channels via strong convergence to semi-circular and circular elements, Random Matrices Theory Appl. 11 (2022), no. 1, 2250012, 36 pp. arXiv:2101.00424
11. K. Fujie and T. Hasebe, The spectra of principal submatrices in rotationally invariant hermitian random matrices and the Markov-Krein correspondence, ALEA Lat. Am. J. Probab. Math. Stat. 19 (2022), 109-123. https://doi.org/10.30757/ALEA.v19-05  (open access)  arXiv:2103.09025
12. T. Hasebe and Y. Ueda, Homomorphisms relative to additive convolutions and max-convolutions: free, boolean and classical cases, Proc. Amer. Math. Soc. 149 (2021), no. 11, 4799-4814. arXiv:2011.10399
13. T. Hasebe and Y. Ueda, Unimodality for free multiplicative convolution with free normal distributions on the unit circle, J. Operator Theory 85 (2021), no. 1, 21-43. arXiv:1903.05327
14. U. Franz, T. Hasebe and S. Schleissinger, Monotone increment processes, classical Markov processes and Loewner chains, Dissertationes Mathematicae 552 (2020), 1-119. online first version
15. Y. Gu, T. Hasebe and P. Skoufranis, Bi-monotonic independence for pairs of algebras, J. Theoret. Probab. 33 (2020), no. 1, 533-566. arXiv:1708.05334
16. T. Hasebe, T. Simon and M. Wang, Some properties of the free stable distributions, Ann. Inst. Henri Poincaré Probab. Stat. 2020, Vol. 56, No. 1, 296-325. published ver.   journal webpage
17. T. Hasebe and K. Szpojankowski, On free Generalized Inverse Gaussian distributions, Complex Analysis and Operator Theory 13 (2019), Issue 7, 3091-3116. arXiv:1710.04572
18. T. Hasebe, N. Sakuma and S. Thorbjørnsen, The normal distribution is freely selfdecomposable, Int. Math. Res. Not. IMRN, vol. 2019, Issue 6, 1758–1787. arXiv:1701.00409
19. T. Hasebe, H.-W. Huang and J.-C. Wang, Limit theorems in bi-free probability theory, Probab. Theory Related Fields 172 (2018), Issue 3–4, 1081-1119. arXiv:1705.05523
20. O. Arizmendi and T. Hasebe, Limit theorems for free Lévy processes, Electron. J. Probab. 23, no. 101 (2018), 36 pp. https://doi.org/10.1214/18-EJP224  (open access)
21. B. Collins, T. Hasebe and N. Sakuma, Free probability for purely discrete eigenvalues of random matrices, J. Math. Soc. Japan 70, No. 3 (2018), 1111-1150. arXiv:1512.08975
22. T. Hasebe and Y. Ueda, Large time unimodality for classical and free Brownian motions with initial distributions, ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), 353-374. https://doi.org/10.30757/ALEA.v15-15  (open access)  arXiv:1710.08240
23. T. Hasebe and N. Sakuma, Unimodality for free Lévy processes, Ann. Inst. Henri Poincaré Probab. Stat. 53, No. 2 (2017), 916-936. arXiv:1508.01285
24. M. Bożejko, W. Ejsmont and T. Hasebe, Noncommutative probability of type D, Internat. J. Math. 28, No. 2 (2017), 1750010 (30 pages). arXiv:1609.01049
25. T. Hasebe and S. Thorbjørnsen, Unimodality of the freely selfdecomposable probability laws, J. Theoret. Probab. 29 (2016), Issue 3, 922-940. arXiv:1309.6776
26. T. Hasebe, Free infinite divisibility for powers of random variables, ALEA Lat. Am. J. Probab. Math. Stat. 13 (2016), no. 1, 309-336. https://doi.org/10.30757/ALEA.v13-13  (open access)  arXiv:1509.08614  Note: The published version contained an error. It was corrected in the arxiv version.
27. O. Arizmendi and T. Hasebe, Free subordination and Belinschi-Nica semigroup, Complex Anal. Oper. Theory 10, No. 3 (2016), 581-603. arXiv:1408.5983
28. O. Arizmendi and T. Hasebe, Classical scale mixtures of Boolean stable laws, Trans. Amer. Math. Soc. 368 (2016), 4873-4905. arXiv:1405.2162
29. N. Asai, M. Bożejko and T. Hasebe, Radial Bargmann representation for the Fock space of type B, J. Math. Phys. 57 (2016), 021702. arXiv:1512.08862
30. T. Hasebe and N. Sakuma, Unimodality of Boolean and monotone stable distributions, Demonstr. Math. 48, No. 3 (2015), 424-439. arXiv:1403.2487 published ver.
31. M. Bożejko, W. Ejsmont and T. Hasebe, Fock space associated to Coxeter groups of type B, J. Funct. Anal. 269, No. 6 (2015), 1769-1795. arXiv:1411.7997
32. O. Arizmendi, T. Hasebe, F. Lehner and C. Vargas, Relations between cumulants in noncommutative probability, Adv. Math. 282 (2015), 56-92. arXiv:1408.2977
33. T. Hasebe, Free infinite divisibility for beta distributions and related ones, Electron. J. Probab. 19 (2014), No. 81, 1-33. https://doi.org/10.1214/EJP.v19-3448  (open access)   arXiv:1305.0924
34. T. Hasebe and A. Kuznetsov, On free stable distributions, Electron. Commun. Probab. 19 (2014), No. 56, 1-12. https://doi.org/10.1214/ECP.v19-3443  (open access)   arXiv:1404.2981
35. T. Hasebe and H. Saigo, On operator-valued monotone independence, Nagoya Math. J. 215 (2014), 151-167. arXiv:1306.0137
36. O. Arizmendi and T. Hasebe, Classical and free infinite divisibility for Boolean stable laws, Proc. Amer. Math. Soc. 142 (2014), 1621-1632. arXiv:1205.1575
37. M. Bożejko and T. Hasebe, On free infinite divisibility for classical Meixner distributions, Probab. Math. Stat. 33, Fasc. 2 (2013), 363-375. arXiv:1302.4885
38. O. Arizmendi and T. Hasebe, Semigroups related to additive and multiplicative, free and Boolean convolutions, Studia Math. 215 (2013), 157-185. arXiv:1105.3344
39. O. Arizmendi and T. Hasebe, On a class of explicit Cauchy-Stieltjes transforms related to monotone stable and free Poisson laws, Bernoulli 19(5B) (2013), 2750-2767. arXiv:1108.3438
40. T. Hasebe, Conditionally monotone independence II, Multiplicative convolutions and infinite divisibility, Compl. Anal. Oper. Theory 7 (2013), 115-134. arXiv:0910.1319
41. O. Arizmendi, T. Hasebe and N. Sakuma, On the law of free subordinators, ALEA, Lat. Amer. J. Probab. Math. Stat. 10, No. 2 (2013), 271-291. arXiv:1201.0311 published ver.
42. T. Hasebe, Fourier and Cauchy-Stieltjes transforms of power laws including stable distributions, Internat. J. Math. 23, No. 3 (2012), 1250041 (21 pages). arXiv:1107.3874
43. T. Hasebe, Analytic continuations of Fourier and Stieltjes transforms and generalized moments of probability measures, J. Theoret. Probab. 25, No. 3 (2012), 756-770. arXiv:1009.1510
44. T. Hasebe and H. Saigo, Joint cumulants for natural independence, Electron. Commun. Probab. 16 (2011), 491-506. http://doi.org/10.1214/ECP.v16-1647  (open access)   arXiv:1005.3900
45. T. Hasebe and H. Saigo, The monotone cumulants, Ann. Inst. Henri Poincaré Probab. Stat. 47, No. 4 (2011), 1160-1170. arXiv:0907.4896
46. T. Hasebe, Differential independence via an associative product of infinitely many linear functionals, Colloq. Math. 124 (2011), 79-94. preprint ver.
47. T. Hasebe, Conditionally monotone independence I, Independence, additive convolutions and related convolutions, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, No. 3 (2011), 465-516. arXiv:0907.5473
48. T. Hasebe, Monotone convolution semigroups, Studia Math. 200 (2010), 175-199. preprint ver.
49. T. Hasebe, Monotone convolution and monotone infinite divisibility from complex analytic viewpoints, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13, No. 1 (2010), 111-131.

Other works

1. P. Gumenyuk, T. Hasebe and J.-L. Pérez, Loewner Theory for Bernstein functions I: evolution families and differential equations. Constr. Approx. 61 (2025), 379-412 https://doi.org/10.1007/s00365-023-09675-9  (open access)  arXiv:2206.04753
2. T. Yamada et al, Construction of normal vector field using the partial differential equations (in Japanese), the Japan Journal of Industrial and Applied Mathematics, Vol. 30, No. 3 (2020), 249-258. published version
3. T. Yamada et al., Topology optimization with geometrical feature constraints based on the partial differential equation system for geometrical features (Overhang constraints considering geometrical singularities in additive manufacturing), Transactions of the JSME (in Japanese), Vol.85, No.877, 2019. published ver.
4. T. Hasebe, T. Miyatani and M. Yoshinaga, Euler characteristic reciprocity for chromatic, flow and order polynomials, Journal of Singularities 16 (2017), 212-227. https://doi.org/10.5427/jsing.2017.16k  (open access)  arXiv:1601.00254
5. T. Hasebe and S. Tsujie, Order quasisymmetric functions distinguish rooted trees, J. Algebraic Combin. 46 (2017), 499-515. arxiv:1610.03908
6. T. Hasebe, White noise analysis on manifolds and the energy representation of a gauge group, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13, No. 4 (2010), 619-627. arXiv:0805.1329
7. T. Hasebe, I. Ojima and H. Saigo, No zero divisor for Wick product in (S)^*, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 2 (2008), 307-311. arXiv:0712.3915

Old preprints

1. T. Hasebe, Free infinite divisibility of measures with rational function densities, preprint, not to be published.

Link

• Department of Mathematics, Hokkaido University