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Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory

2008
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Journal of Statistical Mechanics: Theory and Experiment
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It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point process in d-dimensional Euclidean space for any d, which are special cases of determinantal processes. In particular, we obtain the n-particle correlation functions for any n, which completely specify the point processes. We also demonstrate that

doi:10.1088/1742-5468/2008/11/p11019
fatcat:hmvcpz2yxjfhhohqs4e5yx2ny4