Spectral gap of Boltzmann measures on unit circle

Yutao MA; Zhengliang ZHANG

doi:10.1007/s11464-021-0892-y

Front. Math. China ›› 2021, Vol. 16 ›› Issue (2) : 559 -566. DOI: 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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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 $h ∈ ℝ$ 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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Yutao MA, Zhengliang ZHANG. Spectral gap of Boltzmann measures on unit circle. Front. Math. China, 2021, 16(2): 559-566 DOI:10.1007/s11464-021-0892-y

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