论文信息 - Entropy and Random Vectors

Entropy and Random Vectors

Barron(1) produced a proof of the Central Limit Theorem for real-valued IID random variables, in the sense of convergence in relative entropy. Here, we establish a similar result for independent real-valued random vectors, not necessarily identically distributed. The main developments required are a generalisation of De Bruijn's identity, and various inequalities proposed in ref. 2.

O. Johnson | Y. Suhov

[1] R. A. Leibler,et al. On Information and Sufficiency , 1951 .

[2] J. Linnik. An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions , 1959 .

[3] R. Dobrushin,et al. Absence of breakdown of continuous symmetry in two-dimensional models of statistical physics , 1975 .

[4] A. Barron. ENTROPY AND THE CENTRAL LIMIT THEOREM , 1986 .

[5] E. Carlen,et al. Entropy production by block variable summation and central limit theorems , 1991 .

[6] Phase‐space dynamics and Hermite polynomials of two variables and two indices , 1994 .

[7] O. Johnson. Entropy inequalities and the Central Limit Theorem , 2000 .

[8] Oliver Johnson,et al. Entropy and Convergence on Compact Groups , 2000 .

[9] Oliver Johnson. An Information-Theoretic Central Limit Theorem for Finitely Susceptible FKG Systems , 2001 .