References
- Baraquin, I. (2020). Random walks on finite quantum groups. J. Theor. Probab. 33(3):1715–1736. DOI: 10.1007/s10959-019-00916-x.
- Bekka, B., P. de la, H., Valette, A. (2008). Kazhdan's property (T). New Mathematical Monographs, Cambridge: Cambridge University Press.
- Blackadar, B. (2006). Operator Algebras: Theory of C*-Algebras and Von Neumann Algebras. Berlin, Germany: Springer.
- Borel, E., Chéron, A., Ville, J.A. (1940). Théorie mathématique du bridge: a la portée de tous. Applications de la théorie des probabilités aux jeux de hasard. Valeur pratique et philosophie des probabilités.
- Ceccherini-Silberstein, T., Scarabotti, F., Tolli, F. (2008). Harmonic Analysis on Finite Groups. New York: Cambridge University Press.
- Diaconis, P., Shahshahani, M. (1981). Generating a random permutation with random transpositions. Z. Wahrscheinlichkeitstheorie Verw. Gebiete. 57(2):159–179. DOI: 10.1007/BF00535487.
- Evans, D. E., Høegh-Krohn, R. (1978). Spectral properties of positive maps on C*-algebras. J. London Math. Soc. s2-17(2):345–355. DOI: 10.1112/jlms/s2-17.2.345.
- Fagnola, F., Pellicer, R. (2009). Irreducible and periodic positive maps. COSA. 3(3):407–418. DOI: 10.31390/cosa.3.3.06.
- Franz, U., Gohm, R. (2006). Random walks on finite quantum groups. In: Quantum Independent Increment Processes II, 1866 of Lecture Notes in Math. Berlin, Heidelberg: Springer, pp. 1–32.
- Franz, U., Skalski, A. (2008). On ergodic properties of convolution operators associated with compact quantum groups. Colloq. Math. 113(1):13–23. DOI: 10.4064/cm113-1-2.
- Franz, U., Skalski, A. (2009). On idempotent states on quantum groups. J. Algebra 322(5):1774–1802. DOI: 10.1016/j.jalgebra.2009.05.037.
- Freslon, A. (2019). Cut-off phenomenon for random walks on free orthogonal free groups. Probab. Theory Relat. Fields 174(3-4):731–760. DOI: 10.1007/s00440-018-0863-8.
- Freslon, A. (2020). Positive definite functions and cut-off for discrete groups. Canad. Math. Bull. DOI: 10.4153/S0008439520000466.
- Kac, G. I., Paljutkin, V.G. (1966). Finite group rings. Trudy Moskov. Mat. Obšč. 15:251–284. (English transl. Trans. Moscow Math. Soc. (1967)).
- Kasprzak, P. (2018). Shifts of group-like projections and contractive idempotent functionals for locally compact quantum groups. Int. J. Math. 29(13):1850092.
- Kasprzak, P., Sołtan, P. (2020). The lattice of idempotent states on a locally compact quantum group. Publ. Res. Inst. Math. Sci. 56(1):33–53. DOI: 10.4171/PRIMS/56-1-3.
- Kawada, Y., Itô, K. (1940). On the probability distribution on a compact group I. Proc. Phys. Math. Soc. Jpn. 3(22):977–988.
- Landstand, M. B., Van Daele, A. (2007). Compact and discrete subgroups of algebraic quantum groups, I. arXiv:0702.458.
- Markov, A.A. (1906). Extension of the law of large numbers to dependent events. Bull. Soc. Phys. Math. 2:155–156. (In Russian).
- McCarthy, J.P. (2019). Diaconis–Shahshahani upper bound lemma for finite quantum groups. J. Fourier Anal. Appl. 25(5):2463–2491. DOI: 10.1007/s00041-019-09670-4.
- Murphy, G. J. (1990). C*-Algebras and Operator Theory. Boston: Academic Press.
- Pal, A. (1996). A counterexample on idempotent states on a compact quantum group. Lett. Math. Phys. 37(1):75–77. DOI: 10.1007/BF00400140.
- Rosenthal, J.S. (1994). Random rotation: characters and random walks on SO(N). Ann. Probab. 22(1):398–423. DOI: 10.1214/aop/1176988864.
- Sekine, Y. (1996). An example of finite-dimensional Kac algebras of Kac–Paljutkin type. Proc. Amer. Math. Soc. 124(4):1139–1147. DOI: 10.1090/S0002-9939-96-03199-1.
- Van Daele, A. (1997). The Haar measure on finite quantum groups. Proc. Amer. Math. Soc. 125(12):3489–3500. DOI: 10.1090/S0002-9939-97-04037-9.
- Wang, S. Z. (2009). Simple compact quantum groups I. J. Funct. Anal. 256(10):3313–3341. DOI: 10.1016/j.jfa.2008.10.020.
- Wang, S. (2016). Lp-improving convolution operators on finite quantum groups. Indiana Univ. Math. J. 65(5):1609–1637. DOI: 10.1512/iumj.2016.65.5881.
- Zhang, H. (2019). Idempotent states on Sekine quantum groups. Comm. Algebra 47(10):4095–4113. DOI: 10.1080/00927872.2019.1579335.