Frontiers of Mathematics in China >

2021 , Vol. 16 >Issue 2: 559 - 566

DOI: https://doi.org/10.1007/s11464-021-0892-y

RESEARCH ARTICLE

Spectral gap of Boltzmann measures on unit circle

  • Yutao MA , 1 ,
  • Zhengliang ZHANG 2
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  • 1. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875, China
  • 2. Department of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received date: 01 Apr 2020

Accepted date: 14 Dec 2020

Published date: 15 Apr 2021

Copyright

2021 Higher Education Press
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Abstract

We give a two sided estimate on the spectral gap for the Boltzmann measures μh on the circle. We prove that the spectral gap is greater than 1 for any h∈ℝ and the spectral gap tends to the positive infinity as h→∞ with speed |h|.

Key words： Boltzmann measure; Poincaré inequality; spectral gap; unit circle

Cite this article

Yutao MA , Zhengliang ZHANG . Spectral gap of Boltzmann measures on unit circle[J]. Frontiers of Mathematics in China, 2021 , 16(2) : 559 -566 . DOI: 10.1007/s11464-021-0892-y

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