The Dual Majorizing Measure Theorem for Canonical Processes

Abstract: We completely characterize the boundedness of the log-concave-tailed canonical processes. The corresponding new majorizing measure theorem for log-concave-tailed canonical processes is proved using the new tree structure. Moreover, we introduce the new growth condition. Combining this condition with the dual majorizing measure theorem proven in the paper, we have developed a polynomial-time algorithm for computing expected supremum of the log-concave canonical processes.