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Due to their non-compact nature, traditional spectral analysis techniques face challenges in this setting. However, many practical rendering methods effectively employ compact approximations, suggesting that non-compactness is not an absolute barrier. We show the relevance of such approximations and establish various path integral formulations of their spectrum. These findings enhance the theoretical understanding of light transport and offer new perspectives for improving rendering efficiency and accuracy.<\/jats:p>","DOI":"10.1145\/3774756","type":"journal-article","created":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T11:17:40Z","timestamp":1762255060000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Spectral Theory of Light Transport Operators"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3214-4183","authenticated-orcid":false,"given":"Cyril","family":"Soler","sequence":"first","affiliation":[{"name":"INRIA - Grenoble University","place":["France"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7302-4383","authenticated-orcid":false,"given":"Kartic","family":"Subr","sequence":"additional","affiliation":[{"name":"University of Edinburgh","place":["United Kingdom"]}]}],"member":"320","published-online":{"date-parts":[[2025,12,19]]},"reference":[{"key":"e_1_3_4_2_1","volume-title":"Analytic Methods for Simulated Light Transport","author":"Arvo James","year":"1996","unstructured":"James Arvo. 1996. 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