We prove a dimension-free analogue of Pisier's inequality on the discrete cube due to Ivanisvili/van Handel/Volberg that resolved a conjecture of Enflo. Moreover, we use their results to recover a variant of a theorem due to Eldan/Gross for Boolean functions. Throughout the talk, counterparts to the Gaussian setting will be highlighted.

References:

1. Rademacher type and Enflo type coincide. Ivanisvili/van Handel/Volberg arXiv: 2003.06345
2. On the Eldan-Gross inequality. Ivanisvili/Zhang arXiv: 2407.17864
3. Ramon van Handel's Remarks on the Discrete Cube (lecture notes by G. Rosenthal)