Haonan Zhang

collaborators

4 papers

math.CA2026

A Beckmann boundary form of Talagrand's conjecture on the discrete cube

Paata Ivanisvili, Xinyuan Xie, Haonan Zhang

We introduce the Beckmann boundary of a Boolean function \[ \mathsf{B}(f)=\inf_{\operatorname{div} V=Lf}\mathbb E\|V(x)\|_2. \] Here \[ L=\sum_iD_i,\qquad D_i f(x)=\frac{f(x)-f(x^{…

math.OA2026

Sharp hypercontractivity for free orthogonal quantum groups of Kac type

Haonan Zhang

We prove that the normalized heat semigroup $P_{t} = e^{- t L}$ on every free orthogonal quantum group $O_{F}^{+}$ of Kac type satisfies hypercontractivity with the optimal time. More precis…

math.CA2026

Sharp log-Sobolev inequalities on finite cyclic groups

Xinyuan Xie, Haonan Zhang

Let $Z_{n}$ be the cyclic group equipped with the uniform probability measure $I ¨ $ , and let $A_{I ¨ _{n}}$ be the Laplacian with word length \[ Ï_n(k) = \min(k,n-k). \] We prove…

math.OA2026

Sharp hypercontractivity for free group von Neumann algebras

Xinyuan Xie, Haonan Zhang

In this paper, we settle the problem of optimal hypercontractivity for free group von Neumann algebras. Namely, for $n \geq 2$ and the free group $F_{n}$ on $n$ generators, we…