On Applications of Discrete Isoperimetric and Hypercontractive Inequalities
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fei-yumou415-sm-eecs-2026-thesis.pdf
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Author(s)
Fei, Yumou
Advisor(s)
Minzer, Dor
Rubinfeld, Ronitt
Date Issued
February 2026
Publisher
Massachusetts Institute of Technology
Abstract
Isoperimetric and hypercontractive inequalities are two fundamental tools in analysis. Their discrete counterparts have been widely applied in theoretical computer science, with significant impact on areas such as property testing, computational complexity, and Markov chain analysis. In this thesis, we develop new discrete isoperimetric and hypercontractive inequalities and demonstrate their applications to Markov chain mixing times and lower bounds for streaming algorithms. The emphasis of the thesis will be placed on presenting the additional nontrivial ingredients that enable these inequalities to be applied to the problems of interest, rather than on proving the inequalities themselves. We will also provide a high-level explanation of what makes these inequalities particularly effective in the corresponding problems. The thesis is based on the author’s joint works with Renato Ferreira Pinto Jr., Dor Minzer and Shuo Wang.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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