Chernoff–Hoeffding inequalities and bounded multi-parameter square functions
Release Date： 2025-06-10 Unit： Department of Mathematics
Professor：Prof. Ji Li (Macquarie University, Australia)
Theme：Chernoff–Hoeffding inequalities and bounded multi-parameter square functions
Date：Jun. 23th (Mon) 11:00 a.m. ~ 11:50 a.m.
Location：Hong-Jing Building, M107
Abstract：
We establish Hoeffding inequalities for the summation of atomic functions possessing suitable almost-orthogonality via introducing a new square function and by constructing an iterative algorithm on the scales of this new square function. The main result yields new multi-parameter Hoeffding inequalities, and generalizes those for dyadic martingales. Our square function and the associated algorithm represent a refined design—contrasting with the classical dyadic martingale framework—enabling a layer-by-layer exploitation of multi-scale cancellation phenomena.
As an application, we obtain several equivalent characterizations of our Hoeffding inequalities, including the sharp order of local integrability for our generalized multi-parameter square functions. Our work extends the classical result of Chang–Wilson–Wolff (1985) in one-parameter setting and bridges the gap by resolving the multi-dimensional counterpart of Pipher’s work on the bi-disc (1986).
This talk is mainly based on the recent progress:
Ji Li, Jill Pipher and Liangchuan Wu, “Chernoff–Hoeffding inequalities, almost orthogonality and bounded multi-parameter square functions”, submitted.
Theme：Chernoff–Hoeffding inequalities and bounded multi-parameter square functions
Date：Jun. 23th (Mon) 11:00 a.m. ~ 11:50 a.m.
Location：Hong-Jing Building, M107
Abstract：
We establish Hoeffding inequalities for the summation of atomic functions possessing suitable almost-orthogonality via introducing a new square function and by constructing an iterative algorithm on the scales of this new square function. The main result yields new multi-parameter Hoeffding inequalities, and generalizes those for dyadic martingales. Our square function and the associated algorithm represent a refined design—contrasting with the classical dyadic martingale framework—enabling a layer-by-layer exploitation of multi-scale cancellation phenomena.
As an application, we obtain several equivalent characterizations of our Hoeffding inequalities, including the sharp order of local integrability for our generalized multi-parameter square functions. Our work extends the classical result of Chang–Wilson–Wolff (1985) in one-parameter setting and bridges the gap by resolving the multi-dimensional counterpart of Pipher’s work on the bi-disc (1986).
This talk is mainly based on the recent progress:
Ji Li, Jill Pipher and Liangchuan Wu, “Chernoff–Hoeffding inequalities, almost orthogonality and bounded multi-parameter square functions”, submitted.
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Updated: 2025-06-10
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