Noise Stability on the Boolean Hypercube via a Renormalized Brownian Motion

Eldan, Ronen; Mikulincer, Dan; Raghavendra, Prasad

doi:10.1145/3564246.3585118

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Cited by 3 publications

References 14 publications

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On the $$\Phi $$-stability and related conjectures

2023

Probab. Theory Relat. Fields

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On the $$\Phi $$-stability and related conjectures

2023

Probab. Theory Relat. Fields

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Breakdown of a concavity property of mutual information for non-Gaussian channels

Kireeva,

Mourrat

2024

Information and Inference: A Journal of the IMA

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Let $S$ and $\tilde S$ be two independent and identically distributed random variables, which we interpret as the signal, and let $P_{1}$ and $P_{2}$ be two communication channels. We can choose between two measurement scenarios: either we observe $S$ through $P_{1}$ and $P_{2}$, and also $\tilde S$ through $P_{1}$ and $P_{2}$; or we observe $S$ twice through $P_{1}$, and $\tilde{S}$ twice through $P_{2}$. In which of these two scenarios do we obtain the most information on the signal $(S, \tilde S)$? While the first scenario always yields more information when $P_{1}$ and $P_{2}$ are additive Gaussian channels, we give examples showing that this property does not extend to arbitrary channels. As a consequence of this result, we show that the continuous-time mutual information arising in the setting of community detection on sparse stochastic block models is not concave, even in the limit of large system size. This stands in contrast to the case of models with diverging average degree, and brings additional challenges to the analysis of the asymptotic behavior of this quantity.

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Directed Isoperimetry and Monotonicity Testing: A Dynamical Approach

Pinto

2024

2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)

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Noise Stability on the Boolean Hypercube via a Renormalized Brownian Motion

Cited by 3 publications

References 14 publications

On the $$\Phi $$-stability and related conjectures

On the $$\Phi $$-stability and related conjectures

Breakdown of a concavity property of mutual information for non-Gaussian channels

Directed Isoperimetry and Monotonicity Testing: A Dynamical Approach

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