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math.PR2026
Entropic Inequalities and Limit Theorems in Boolean Probability
Kewei Pan
We study Boolean entropy and Fisher information in information inequalities and the Boolean central limit theorem. We prove a fractional Stam inequality for the Boolean Fisher info…
math.PR2026
Functional inequalities for Boolean entropy
Guillaume Cébron, Kewei Pan
Building on the recently introduced notion of Boolean entropy, we define the corresponding Boolean Fisher information via a de Bruijn identity. We study the monotonicity of this Fi…
math.PR2025
A Boolean analogue of Shannon's entropy and monotonicity problem
Kewei Pan
In this article, we introduce a notion of entropy for Boolean independence analogous to the Shannon's entropy and Voiculescu's free entropy through the study of asymptotic probabil…