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Here, we develop a general theoretical framework for diffusion-mediated autocatalytic processes at surfaces. We derive a nonlinear renewal-type integral equation for the generating function of the population size, which provides access to its full probability distribution and integer moments. We further establish an equivalent description in terms of a Fokker\u2013Planck equation with nonlinear Robin boundary conditions that encode surface autocatalytic reactions. Our results identify universal asymptotic regimes and provide a unified framework to predict when surface activity promotes extinction or explosive growth of the population. The developed quantitative framework opens new avenues for analyzing catalytic efficiency, metabolic regulation, and population persistence in spatially heterogeneous environments.<\/jats:p>","DOI":"10.1063\/5.0351634","type":"journal-article","created":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T12:23:30Z","timestamp":1788265410000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Reaction\u2013diffusion processes with surface autocatalysis"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6273-9164","authenticated-orcid":false,"given":"Denis S.","family":"Grebenkov","sequence":"first","affiliation":[{"name":"Laboratoire de Physique de la Mati\u00e8re Condens\u00e9e, CNRS\u2013Ecole Polytechnique, Institut Polytechnique de Paris , Palaiseau 91120,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,1]]},"reference":[{"key":"2026090108222234200_c1","volume-title":"Diffusion and Reaction in Disordered Systems","year":"2000"},{"key":"2026090108222234200_c2","doi-asserted-by":"crossref","DOI":"10.1142\/q0209","volume-title":"Chemical Kinetics: Beyond the Textbook","author":"Lindenberg","year":"2019"},{"key":"2026090108222234200_c3","doi-asserted-by":"publisher","first-page":"2446","DOI":"10.1103\/physreva.19.2446","article-title":"Importance of classical diffusion in NMR studies of water in biological cells","volume":"19","year":"1979","journal-title":"Phys. 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