Haonan Zhang

activity

20152026

most citedComplete gradient estimates of quantum Markov semigroups

10 citations · 21 across the 10 of their papers we have counts for

collaborators

10 papers

math.FA2026

The König constant is one

Xinyuan Xie, Haonan Zhang

For each $N \geq 1$ , consider the normalized König bilinear form $B_{K} : L_{\infty} (R^{N}) \times L_{\infty} (R^{N}) \to R$ given by \[ B_{\mathrm K}(f,g):=\frac{1…

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…

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

Let $N \geq 2$ , let $F \in G L_{N} (C)$ , and let $O_{F}^{+}$ be the associated free orthogonal quantum group of Kac type, with tracial Haar state $h$ . We prove that, for $1<p\leq r<\i…

math.CA2026

Sharp log-Sobolev inequalities and quartic stability on finite cyclic groups

Xinyuan Xie, Haonan Zhang

Let $Z_{n}$ be the cyclic group equipped with the uniform probability measure $π$ , and let $A_{ψ_{n}}$ be the Laplacian with word length $ψ_{n} (k) = min (k, n - k) .$ For every $…

math.FA2024

Intertwining Curvature Bounds for Graphs and Quantum Markov Semigroups

Florentin Münch, Melchior Wirth, Haonan Zhang

Based on earlier work by Carlen-Maas and the second- and third-named author, we introduce the notion of intertwining curvature lower bounds for graphs and quantum Markov semigroups…

math.FA2022★ 3 cited

Quantum Talagrand, KKL and Friedgut's theorems and the learnability of quantum Boolean functions

Cambyse Rouzé, Melchior Wirth, Haonan Zhang

We extend three related results from the analysis of influences of Boolean functions to the quantum setting, namely the KKL Theorem, Friedgut's Junta Theorem and Talagrand's varian…

math.OA2021

Curvature-dimension conditions for symmetric quantum Markov semigroups

Melchior Wirth, Haonan Zhang

Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Ma…

math.OA2020★ 10 cited

Complete gradient estimates of quantum Markov semigroups

Melchior Wirth, Haonan Zhang

In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which impli…

math.OA2015★ 8 cited

Hypercontractivity of heat semigroups on free quantum groups

Uwe Franz, Guixiang Hong, François Lemeux +2

In this paper we study two semigroups of completely positive unital self-adjoint maps on the von Neumann algebras of the free orthogonal quantum group $O_{N}^{+}$ and the free permutat…