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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 be the cyclic group equipped with the uniform probability measure , and let be the Laplacian with word length For every $…
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 . This follows up on previous work, where such bounds were established for n…