9 papers
Upper-shadow comparisons on the slice and the Frankl--Tokushige product conjectures
Fan Chang, Hong Liu, Miao Liu
Let , and let be the family of all -sets containing a member of . Writing $μ_k(\mathcal{F})=|\…
The sharp diagonal spectral correlation inequality on the discrete cube
Fan Chang, Hong Liu, Miao Liu
We prove the sharp diagonal spectral correlation conjecture of Friedgut, Kahn, Kalai and Keller, proposed in their Fourier-analytic approach to Chvátal's conjecture. For every pai…
A sharp -biased product bound for -cross-intersecting families
Fan Chang, Hong Liu, Miao Liu
We prove a sharp product theorem for -cross-intersecting families in the -biased measure. If , , and $\mathcal{F}_1,\dots,\mathcal{F}_r\subset…
A spectral correlation inequality for increasing Boolean functions
Fan Chang
Talagrand's correlation inequality provides a quantitative strengthening of the Harris--Kleitman inequality for increasing Boolean functions. Motivated by a Fourier-analytic conjec…
Talagrand-Type Correlation Inequalities for Submodular and Supermodular Functions on the Hypercube
Fan Chang, Yu Chen
Talagran's correlation inequality provides quantitative lower bounds on the covariance of two increasing Boolean functions in terms of their coordinate influences, but, in general,…
The Boolean surface area of polynomial threshold functions
Fan Chang, Joseph Slote, Alexander Volberg +1
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work o…