A solvable mixed charge ensemble on the line: global results

• 成果类型: Article
• 署名作者: Rider, Brian; Sinclair, Christopher D.; Xu, Yuan
• 署名单位: University of Colorado System; University of Colorado Boulder; University of Oregon
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0394-z
• 发表日期: 2013
• 页码: 127-164
• 关键词: Polynomials

摘要

We consider an ensemble of interacting charged particles on the line consisting of two species of particles with charge ratio 2:1 in the presence of an external field. With the total charge fixed and the system held at temperature corresponding to beta = 1, it is proved that the particles form a Pfaffian point process. When the external field is quadratic (the harmonic oscillator potential), we produce the explicit family of skew-orthogonal polynomials necessary to simplify the related matrix kernels. In this setting a variety of limit theorems are proved on the distribution of the number as well as the spatial density of each species of particle as the total charge increases to infinity. Connections to Ginibre's real ensemble of random matrix theory are highlighted throughout.