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Spectral gap of Boltzmann measures on unit circle

Authors:	Yutao MA Zhengliang ZHANG

Institution:	¹. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875, China². Department of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

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

Keywords:	Boltzmann measure Poincaré inequality spectral gap unit circle

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