bibkey: rioulbeguinot2025informationcombining
authors: O. Rioul and J. Béguinot
year: 2025
title: "The role of Mrs. Gerber's Lemma for evaluating the information leakage of secret sharing schemes"
doi: null
url: https://cea.hal.science/hal-05074668v1
claim: "§4, p. 20, Proposition 1 numerically states that u_α is decreasing for α ∈ [−1, 1.5]; Remark 6 identifies α̂ = 3/2 in Hirche's Conjecture IV.6."
strata_touched:
  - D5/S3/Entropy/RenyiCombining/HircheArimotoCombining
license: citation-only
triage: anchor

Rioul–Béguinot on Arimoto information combining

O. Rioul and J. Béguinot, “The role of Mrs. Gerber’s Lemma for evaluating the information leakage of secret sharing schemes”, Barron Festschrift (Springer), HAL hal-05074668v1 (2025).

Locator

Source: https://cea.hal.science/hal-05074668v1, §4, p. 20, Proposition 1 and Remark 6.

Proposition 1:

Proposition 1 It is easily checked numerically (see Figure 3) that: … if α ∈ [−1, 1.5] then u_α is decreasing; …

Remark 6:

Remark 6 This Proposition answers the open question left as a conjecture by Hirche [20, Conjecture IV.6.], where we established that α̂ = 3/2 in his conjecture.

Their support is a numerical sign plot produced with SageMath (Figure 3); no proof is given there. The proposition and remark supply the prior numerical statement of the threshold $\hat{\alpha }=3/2$, without proving the sign throughout the real parameter and bias domains.

ASSUMED-UNVERIFIED

Citation indexes and subsequent literature have not been exhaustively checked; this note does not establish bibliographic priority or the absence of a later analytic proof.