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== Higher-order correlation functions ==
It has been noted that radial distribution functions alone are insufficient to characterize structural information. Distinct point processes may possess identical or practically indistinguishable radial distribution functions, known as the degeneracy problem.<ref>{{Cite journal|last1=Stillinger|first1=Frank H.|last2=Torquato|first2=Salvatore|date=2019-05-28|title=Structural degeneracy in pair distance distributions|url=https://aip.scitation.org/doi/10.1063/1.5096894|journal=The Journal of Chemical Physics|volume=150|issue=20|pages=204125|doi=10.1063/1.5096894|pmid=31153177|bibcode=2019JChPh.150t4125S|s2cid=173995240|issn=0021-9606|doi-access=free|url-access=subscription}}</ref><ref>{{Cite journal|last1=Wang|first1=Haina|last2=Stillinger|first2=Frank H.|last3=Torquato|first3=Salvatore|date=2020-09-23|title=Sensitivity of pair statistics on pair potentials in many-body systems|journal=The Journal of Chemical Physics|volume=153|issue=12|pages=124106|doi=10.1063/5.0021475|pmid=33003740|bibcode=2020JChPh.153l4106W|s2cid=222169131|issn=0021-9606|doi-access=free}}</ref> In such cases, higher order correlation functions are needed to further describe the structure.
Higher-order distribution functions <math>\textstyle g^{(k)}</math> with <math>\textstyle k > 2</math> were less studied, since they are generally less important for the thermodynamics of the system; at the same time, they are not accessible by conventional scattering techniques. They can however be measured by [[coherent scattering|coherent X-ray scattering]] and are interesting insofar as they can reveal local symmetries in disordered systems.<ref>{{Cite journal | last1 = Wochner | first1 = P. | last2 = Gutt | first2 = C. | last3 = Autenrieth | first3 = T. | last4 = Demmer | first4 = T. | last5 = Bugaev | first5 = V. | last6 = Ortiz | first6 = A. D. | last7 = Duri | first7 = A. | last8 = Zontone | first8 = F. | last9 = Grubel | first9 = G. | doi = 10.1073/pnas.0905337106 | last10 = Dosch | first10 = H. | title = X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter | journal = Proceedings of the National Academy of Sciences | volume = 106 | issue = 28 | pages = 11511–4 | year = 2009 | pmid = 20716512| pmc = 2703671|bibcode = 2009PNAS..10611511W | doi-access = free }}</ref>
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