Hypercontractivity and logarithmic-Sobolev inequalities

به سوی علوم ریاضی

Volume 1, Issue 1, September 2021, Pages 40-68   

Document Type: Expository article (original)

DOI: 10.22067/tmsj.2021.68541.1005

Author

Salman Beigi^*

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

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

References