One classical approach for the proof of the central limit theorem is via the characteristic functions, which is the Fourier transform of the probability density. In this talk, I will discuss an approach to study the global fluctuations of random N-particle systems using the Jack polynomials, which can be viewed as the Fourier transform on certain locally compact groups. I will first introduce the Jack polynomials, and give some examples of random N-particle systems related Jack polynomials. Then I will introduce the Jack generating functions, which generalize the Schur generating functions introduced by Bufetov and Vadim. Finally, I will explain how to extract information of the measure by applying certain operators on the Jack generating functions, and survey some previous works using this idea.