4 papers
The optimal hypercontractive constants for and biased Bernoulli random variables
Jie Cao, Shilei Fan, Yong Han +2
We resolve a folklore problem of determining the optimal hypercontractive constants for the cyclic group for all . More p…
Microcanonical cascades and random homeomorphisms
Xinxin Chen, Yong Han, Yanqi Qiu +1
We give a complete solution to the Mandelbrot-Kahane problem for the microcanonical cascade measures by determing their exact Fourier dimensions. We also discuss the Frostman regul…
Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales
Xinxin Chen, Yong Han, Yanqi Qiu +1
We solve a long-standing open problem of determining the Fourier dimension of the Mandelbrot canonical cascade measure (MCCM). This problem of significant interest was raised by Ma…
UCB Exploration for Fixed-Budget Bayesian Best Arm Identification
Rong J. B. Zhu, Yanqi Qiu
We study best-arm identification (BAI) in the fixed-budget setting. Adaptive allocations based on upper confidence bounds (UCBs), such as UCBE, are known to work well in BAI. Howev…