On Classical Analogues of Free Entropy

  title={On Classical Analogues of Free Entropy},
  author={Alice Guionnet and Dimitri Shlyakhtenko},
Abstract. We define a classical probability analog of Voiculescu’s free entropy dimension that we shall call the classical probability entropy dimension. We show that the classical probability entropy dimension is related with diverse other notions of dimension. First, it equals the fractal dimension. Second, if one extends Bochner’s inequalities to a measure by requiring that microstates around this measure asymptotically satisfy the classical Bochner’s inequalities, then we show that the… CONTINUE READING
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