A Note on Physical Dependence and Mixing Conditions for Triangular Arrays

Under mild structural assumptions and regularity conditions on the marginal and conditional densities, an explicit bound on the $\beta$-mixing coefficients in terms of the physical dependence measure is provided. Consequently, weak physical dependence implies $\beta$-mixing and strong mixing for triangular arrays, complementing Hill (2025), who proved the converse implication under moment assumptions.