Establishes the bound P(P_τ f > η ∫f dμ) ≤ c_τ (log log η)^{3/2} / (η √(log η)) for the heat semigroup on the hypercube, resolving Talagrand's convolution conjecture up to a dimension-free loglog factor.
Springer Science & Business Media
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Talagrand's convolution conjecture up to loglog via perturbed reverse heat
Establishes the bound P(P_τ f > η ∫f dμ) ≤ c_τ (log log η)^{3/2} / (η √(log η)) for the heat semigroup on the hypercube, resolving Talagrand's convolution conjecture up to a dimension-free loglog factor.