Xinyuan Xie

activity

20242026

collaborators

8 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.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.PR2026

Grokability in five inequalities

Paata Ivanisvili, Xinyuan Xie

In this note, we report five mathematical discoveries made in collaboration with Grok, all of which have been subsequently verified by the authors. These include an improved lower…

math.CA2026

Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent

Polona Durcik, Paata Ivanisvili, Joris Roos +1

A sharp isoperimetric inequality for the Hamming cube is proved at the critical exponent $β = \frac{1}{2}$ . This follows up on previous work, where such bounds were established for $β$ n…

math.PR2025

Counterexample to majority optimality in NICD with erasures

Paata Ivanisvili, Xinyuan Xie

We asked GPT-5 Pro to look for counterexamples among a public list of open problems (the Simons ``Real Analysis in Computer Science'' collection). After several numerical experimen…

math.FA2024

Jackson's inequality on the hypercube

Paata Ivanisvili, Roman Vershynin, Xinyuan Xie

We investigate the best constant $J (n, d)$ such that Jackson's inequality \[ \inf_{\mathrm{deg}(g) \leq d} \|f - g\|_{\infty} \leq J(n,d) \, s(f), \] holds for all functions $f$ on…