engleski

Majorization, Csiszár divergence and Zipf- Mandelbrot law

In this paper we show how the Shannon entropy is connected to the theory of majorization. They are both linked to the measure of disorder in a system. However, the theory of majorization usually gives stronger criteria than the entropic inequalities. We give some generalized results for majorization inequality using Csiszár f-divergence. This divergence, applied to some special convex functions, reduces the results for majorization inequality in the form of Shannon entropy and the Kullback-Leibler divergence. We give several applications by using the Zipf-Mandelbrot law.

majorization inequality ; Csiszár f-divergence ; Shannon entropy ; Kullback-Leibler divergence ; Zipf-Mandelbrot law

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