Hypercontractivity and logarithmic-Sobolev inequalities

Document Type : Expository article (original)

Author

• Salman Beigi

School of Mathematics, Institute for Research in Fundamental Sciences (IPM)

10.22067/tmsj.2021.68541.1005

Abstract

Hypercontractivity and logarithmic-Sobolev inequalities are important tools in mathematics and have numerous applications in analysis, probability theory, geometry, computer science and information theory. In this paper, basic notions and concepts of this theory are discussed and some applications are presented.

Keywords

• Hypercontractivity inequality
• Log-Sobolev inequality
• Markov semigroup
• Mixing time

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