7 papers
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^{…
Sharp log-Sobolev inequalities on finite cyclic groups
Xinyuan Xie, Haonan Zhang
Let be the cyclic group equipped with the uniform probability measure , and let be the Laplacian with word length \[ Ï_n(k) = \min(k,n-k). \] We prove…
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 and the free group on generators, we…
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…
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 . This follows up on previous work, where such bounds were established for …
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…