关于二维弱约束库仑气体的大偏差的一个注记
A Note on Large Deviations for 2D Coulomb Gas with Weakly Confining Potential
摘要：
研究了库仑气体在弱增长假设下的经验测度，建立了经验测度的大偏差原理。因此，经验措施被认为是收敛到一个非随机的限制措施，其特征在于从对数位势论的变分原理，它可能没有紧凑的支持。大偏差上界的证明是基于一个紧化过程，这可能有助于进一步的大偏差原则。
英文摘要：
We investigate a Coulomb gas in a potential satisfying a weaker growth assumption than usual and establish a large deviation principle for its empirical measure. As a consequence the empirical measure is seen to converge towards a non-random limiting measure, characterized by a variational principle from logarithmic potential theory, which may not have compact support. The proof of the large deviation upper bound is based on a compactification procedure which may be of help for further large deviation principles.
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