Fan Chang

collaborators

10 papers

math.CO2026

Upper-shadow comparisons on the slice and the Frankl--Tokushige product conjectures

Fan Chang, Hong Liu, Miao Liu

Let $F \subseteq (k [ n ])$ , and let $\partial_{k \to ℓ} F$ be the family of all $ℓ$ -sets containing a member of $F$ . Writing $μ_k(\mathcal{F})=|\…

math.CO2026

Quantitative bounds for regular $3$ -wise intersecting families

Fan Chang

Frankston, Kahn and Narayanan proved that every regular increasing $3$ -wise intersecting family of subsets of $[n]$ has cardinality $o (2^{n})$ using Friedgut's junta theorem. We give…

math.CO2026

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 pair…

math.CO2026

A sharp $p$ -biased product bound for $r$ -cross-intersecting families

Fan Chang, Hong Liu, Miao Liu

We prove a sharp product theorem for $r$ -cross-intersecting families in the $p$ -biased measure. If $r \geq 2$ , $0 \leq p \leq \frac{r - 1}{r}$ , and $\mathcal{F}_1,\dots,\mathcal{F}_r\subset…

math.CO2026

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…

cs.CC2026

The estimates for Boolean surface area of polynomial threshold functions

Fan Chang, Joseph Slote, Alexander Volberg +2

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…

math.FA2026

Quantum Talagrand-type Inequalities via Variance Decay

Fan Chang, Peijie Li

We establish dimension-free quantum Talagrand-type inequalities with explicit constants on the quantum Boolean cube, via a unified variance-decay perspective. For individual observ…

math.CO2025

A Lower Bound for the Fourier Entropy of Boolean Functions on the Biased Hypercube

Fan Chang

We study Boolean functions on the $p$ -biased hypercube $({0, 1}^{n}, μ_{p}^{n})$ through the lens of Fourier (spectral) entropy, i.e. the Shannon entropy of the squared $p$ -biased Fourie…

math.CO2025

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,…

math.CO2025

VC-Dimension vs Degree: An uncertainty principle for Boolean functions

Fan Chang, Yijia Fang

We prove a support--shattering uncertainty principle for functions on the Boolean cube. Let $F$ be any field and let $f : {0, 1}^{n} \to F$ be nonzero. If $x^{S}$ is a m…

Upper-shadow comparisons on the slice and the Frankl--Tokushige product conjectures

Quantitative bounds for regular 3-wise intersecting families

The sharp diagonal spectral correlation inequality on the discrete cube

A sharp p-biased product bound for r-cross-intersecting families

A spectral correlation inequality for increasing Boolean functions

The estimates for Boolean surface area of polynomial threshold functions

Quantum Talagrand-type Inequalities via Variance Decay

A Lower Bound for the Fourier Entropy of Boolean Functions on the Biased Hypercube

Talagrand-Type Correlation Inequalities for Submodular and Supermodular Functions on the Hypercube

VC-Dimension vs Degree: An uncertainty principle for Boolean functions

Quantitative bounds for regular $3$ -wise intersecting families

A sharp $p$ -biased product bound for $r$ -cross-intersecting families