Các đại lượng tương đương của entropy và thước đo thông tin Fisher trong lý thuyết xác suất tự do, I

Akhiezer, N.I.: The classical moment problem (in Russian) Moscow, 1961 Balian, R.: Random matrices and information theory. Nuovo Cimento,LVIIB, No. 1, 183–193 (1968) Barron, A.R.: Entropy and the central limit theorem. Ann. Prob.14(1), 336–342 (1986) Bercovici, H., Voiculescu, D.: Levy-Hinčin type theorems for multiplicative and additive free convolution. Pacific J. Math.153, No. 2, 217–248 (1992) Bercovici, H., Voiculescu, D.: Free convolution of measures with unbounded support. Preprint, Berkeley 1992 Carlen, E.A., Soffer, A.: Entropy production by block variable summation and central limit theorems. Commun. Math. Phys.140, 339–371 (1991) Duren, P.L.: Univalent functions. Berlin, Heidelberg, New York: Springer Verlag, 1983 Dykema, K.J.: On certain free product factors via an extended matrix model. J. Funct. Anal. (to appear) Garnett, J.B.: Bounded analytic functions. New York: Academic Press, 1981 Gelfand, I.M., Shilov, G.E.: Generalized functions. I (in Russian). Second edition. Moscow: Fizmatgiz, 1959 Kullback, S.: Information theory and statistics. New York: Dover Publications Inc., 1968 Landkof, N.S.: Foundations of modern potential theory. Berlin, Heidelberg, New York: Springer 1972 Lieb, E.: Convex Trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math.11, 267–288 (1973) Maassen, H.: Addition of freely independent Random variables. J. Funct. Anal.106, 409–438 (1992) Mehta, M.L.: Random matrices and the statistical theory of energy levels. Academic Press Mushkhelishvili, N.I.: Singular integral equations. Groningen: Noordhoff 1953 Nica, A.: Asymptotically free families of Random unitaries in symmetric groups. Pacific J. Math. (to appear) Popa, S.: Orthogonal pairs of *-subalgebras in finite von Neumann algebras. J. Operator Theory9, 253–268 (1983) Radulescu, F.: The fundamental group of ℒ(F ∞) is ℝ+\{0}. J. Am. Math. Soc. (to appear) Radulescu, F.: Stable equivalence of the weak closures of free groups convolution algebras. Preprint Ruelle, D.: Statistical mechanics. New York: Benjamin 1969 Simon, B.: Trace ideals and their applications. Cambridge: Cambridge Univ. Press. 1979 Stam, A.J.: Some Inequalities satisfied by the quantities of information of Fisher and Shannon. Information and Control2, 101–112 (1959) Tsuji, M.: Potential Theory in modern function theory. Tokyo: Maruzen 1959 Voiculescu, D.: Symmetries of some reduced free productC *-algebras. In: Operator algebras and their connections with topology and ergodic theory. Lecture Notes in Math., vol. 1132. Berlin, Heidelberg, New York: Springer, pp. 556–588 (1985) Voiculescu, D.: Addition of certain non-commuting random variables. J. Funct. Anal.66, No. 3, 323–346 (1986) Voiculescu, D.: Multiplication of certain non-commuting random variables. J. Operator Theory18, 223–235 (1987) Voiculescu, D.: Operations on certain non-commutative operator-valued random variables. INCREST Preprint No. 42/1986, Bucharest Voiculescu, D.: Limit laws for random matrices and free products. Invent. Math.104, 201–220 (1991) Voiculescu, D.: Circular and semi-circular systems and free product factors. In: Operator algebras, unitary representations, enveloping algebras and invariant theory. Progress in Math., vol. 92, Birkhäuser, Boston, pp. 45–60 (1990) Voiculescu, D.: Free Non-commutative random variables, random matrices and theII 1-factors of free groups. Quantum probability and related topics. VI. Accardi, L. (ed.) Singapore: World Scientific, pp. 473–487 (1991) Wigner, E.P.: Characteristic vectors of bordered matrices with infinite dimensions. Ann. Math.62, 548–564 (1955) Wigner, E.P.: On the distribution of the roots of certain symmetric matrices. Ann. Math.67, 325–327 (1958)