[{"file_date_updated":"2026-10-19T07:33:58Z","OA_place":"publisher","researchdata_availability":"no","mathsc":["05C80"],"date_updated":"2026-10-19T07:39:17Z","das_tickbox":"0","oa_version":"Published Version","ddc":["500"],"volume":36,"publication":"Annals of Applied Probability","author":[{"last_name":"Hollom","first_name":"Lawrence","full_name":"Hollom, Lawrence"},{"id":"9aa8388e-d003-11ee-8458-c4c1d7447977","full_name":"Lichev, Lyuben","first_name":"Lyuben","last_name":"Lichev"},{"first_name":"Adva","last_name":"Mond","full_name":"Mond, Adva"},{"last_name":"Portier","first_name":"Julien","full_name":"Portier, Julien"},{"first_name":"Yiting","last_name":"Wang","id":"1917d194-076e-11ed-97cd-837255f88785","full_name":"Wang, Yiting"}],"title":"Monotonicity and decompositions of random regular graphs","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (in subscription journal)","citation":{"ieee":"L. Hollom, L. Lichev, A. Mond, J. Portier, and Y. Wang, “Monotonicity and decompositions of random regular graphs,” <i>Annals of Applied Probability</i>, vol. 36, no. 5. Institute of Mathematical Statistics, pp. 4716–4738, 2026.","chicago":"Hollom, Lawrence, Lyuben Lichev, Adva Mond, Julien Portier, and Yiting Wang. “Monotonicity and Decompositions of Random Regular Graphs.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2026. <a href=\"https://doi.org/10.1214/26-AAP2345\">https://doi.org/10.1214/26-AAP2345</a>.","short":"L. Hollom, L. Lichev, A. Mond, J. Portier, Y. Wang, Annals of Applied Probability 36 (2026) 4716–4738.","mla":"Hollom, Lawrence, et al. “Monotonicity and Decompositions of Random Regular Graphs.” <i>Annals of Applied Probability</i>, vol. 36, no. 5, Institute of Mathematical Statistics, 2026, pp. 4716–38, doi:<a href=\"https://doi.org/10.1214/26-AAP2345\">10.1214/26-AAP2345</a>.","ista":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. 2026. Monotonicity and decompositions of random regular graphs. Annals of Applied Probability. 36(5), 4716–4738.","apa":"Hollom, L., Lichev, L., Mond, A., Portier, J., &#38; Wang, Y. (2026). Monotonicity and decompositions of random regular graphs. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/26-AAP2345\">https://doi.org/10.1214/26-AAP2345</a>","ama":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. Monotonicity and decompositions of random regular graphs. <i>Annals of Applied Probability</i>. 2026;36(5):4716-4738. doi:<a href=\"https://doi.org/10.1214/26-AAP2345\">10.1214/26-AAP2345</a>"},"article_type":"original","page":"4716-4738","day":"01","quality_controlled":"1","intvolume":"        36","oa":1,"project":[{"grant_number":"101076777","name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"},{"_id":"e19fef4c-1f3d-11f0-ac04-b8b1af6886d8","grant_number":"E624","name":"THRESHOLDS IN SEMI-RANDOM PROCESSES AND GRAPH EMBEDDINGS"}],"keyword":["Random regular graphs","coupling","contiguity","total variation distance","decomposition"],"doi":"10.1214/26-AAP2345","_id":"23155","month":"10","file":[{"date_updated":"2026-10-19T07:33:58Z","content_type":"application/pdf","checksum":"46101e61d29cf40f0a204801d15a848f","file_size":320593,"relation":"main_file","file_name":"2026_AnnalsAppliedProbability_Hollom.pdf","access_level":"open_access","file_id":"23165","creator":"dernst","date_created":"2026-10-19T07:33:58Z","success":1}],"publisher":"Institute of Mathematical Statistics","external_id":{"arxiv":["2505.22875"]},"publication_status":"published","has_accepted_license":"1","year":"2026","abstract":[{"text":"In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we\r\nshow that, for a wide range of parameters d1 ≤ d2, there exists a coupling of\r\nG(n,d1) and G(n,d2) satisfying that G(n,d1) ⊆ G(n,d2) with high probability, confirming a conjecture of Gao, Isaev and McKay in a new regime.\r\nOur contributions include new tools for analysing contiguity and total variation distance between random regular graph models, a novel procedure for\r\ngenerating unions of random edge-disjoint perfect matchings, and refined estimates of Gao’s bounds on the number of perfect matchings in random regular graphs. In addition, we make progress towards another conjecture of Isaev,\r\nMcKay, Southwell and Zhukovskii.","lang":"eng"}],"OA_type":"hybrid","date_created":"2026-10-18T22:01:52Z","publication_identifier":{"issn":["1050-5164"],"eissn":["2168-8737"]},"department":[{"_id":"MaKw"},{"_id":"GradSch"}],"scopus_import":"1","date_published":"2026-10-01T00:00:00Z","acknowledgement":"We are grateful to Béla Bollobás, to Matthew Kwan and to Fabio\r\nToninelli for their helpful comments and suggestions, and to Nicholas Wormald for useful\r\nremarks on a preliminary version of this work and pointing us towards the reference [29].\r\nThe authors would also like to thank several anonymous referees for many useful suggestions,\r\nincluding pointing out that Lemma 2.10 already appeared in [11].\r\nPart of this research was done during a visit of the fourth author to IST Austria. We thank\r\nIST Austria for its hospitality.\r\nFor open access purposes, the authors have applied a CC BY public copyright license to\r\nany author accepted manuscript version arising from this submission. L. Hollom was supported by the Internal Graduate Studentship of Trinity College, Cambridge.\r\nL. Lichev was supported by the Austrian Science Fund (FWF) grant No. 10.55776/ESP624.\r\nA. Mond was supported by UK Research and Innovation grant MR/W007320/2. Wang was\r\nsupported by the ERC Starting Grant “RANDSTRUCT” No. 101076777.","status":"public","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1214/26-AAP2345","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"PlanS_conform":"1","issue":"5","arxiv":1,"supplementarymaterial":"no"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"fulldoi":"https://doi.org/10.1093/aobpla/plv092","pmid":1,"article_number":"plv092","date_published":"2015-07-27T00:00:00Z","scopus_import":"1","DOAJ_listed":"1","language":[{"iso":"eng"}],"status":"public","OA_type":"gold","date_created":"2026-07-27T12:30:25Z","abstract":[{"lang":"eng","text":"Most of the currently experienced global environmental changes (rising atmospheric CO2 concentrations, warming, altered amount and pattern of precipitation, and increased nutrient load) directly or indirectly affect ecosystem surface energy balance and plant transpiration. As a consequence, the relative humidity of the air surrounding the vegetation changes, thus creating a feedback loop whose net effect on transpiration and finally productivity is not trivial to quantify. Forcedly, in any global change experiment with the above drivers, we can only treat small plots, or ‘islands’, of vegetation. This means that the treated plots will likely experience the ambient humidity conditions influenced by the surrounding, non-treated vegetation. Experimental assessments of global change effects will thus systematically lack modifications originating from these potentially important feedback mechanisms, introducing a bias of unknown magnitude in all measurements of processes directly or indirectly depending on plant transpiration. We call this potential bias the ‘island effect’. Here, we discuss its implications in various global change experiments with plants. We also suggest ways to complement experiments using modelling approaches and observational studies. Ultimately, there is no obvious solution to deal with the island effect in field experiments and only models can provide an estimate of modification of responses by these feedbacks. However, we suggest that increasing the awareness of the island effect among both experimental researchers and modellers will greatly improve the interpretation of vegetation responses to global change."}],"year":"2015","publication_identifier":{"eissn":["2041-2851"]},"_id":"22585","month":"07","publication_status":"published","external_id":{"pmid":["26216468"]},"publisher":"Oxford University Press","oa":1,"intvolume":"         7","quality_controlled":"1","keyword":["DGVM","Elevated CO2","FACE","Hydrology","Land–atmosphere coupling","Vegetation feedback effects","Warming"],"doi":"10.1093/aobpla/plv092","main_file_link":[{"url":"https://doi.org/10.1093/aobpla/plv092","open_access":"1"}],"citation":{"ama":"Leuzinger S, Fatichi S, Cusens J, Körner C, Niklaus PA. The ‘island effect’ in terrestrial global change experiments: a problem with no solution? <i>AoB Plants</i>. 2015;7. doi:<a href=\"https://doi.org/10.1093/aobpla/plv092\">10.1093/aobpla/plv092</a>","apa":"Leuzinger, S., Fatichi, S., Cusens, J., Körner, C., &#38; Niklaus, P. A. (2015). The ‘island effect’ in terrestrial global change experiments: a problem with no solution? <i>AoB Plants</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/aobpla/plv092\">https://doi.org/10.1093/aobpla/plv092</a>","ista":"Leuzinger S, Fatichi S, Cusens J, Körner C, Niklaus PA. 2015. The ‘island effect’ in terrestrial global change experiments: a problem with no solution? AoB Plants. 7, plv092.","mla":"Leuzinger, Sebastian, et al. “The ‘Island Effect’ in Terrestrial Global Change Experiments: A Problem with No Solution?” <i>AoB Plants</i>, vol. 7, plv092, Oxford University Press, 2015, doi:<a href=\"https://doi.org/10.1093/aobpla/plv092\">10.1093/aobpla/plv092</a>.","short":"S. Leuzinger, S. Fatichi, J. Cusens, C. Körner, P.A. Niklaus, AoB Plants 7 (2015).","chicago":"Leuzinger, Sebastian, Simone Fatichi, Jarrod Cusens, Christian Körner, and Pascal A. Niklaus. “The ‘Island Effect’ in Terrestrial Global Change Experiments: A Problem with No Solution?” <i>AoB Plants</i>. Oxford University Press, 2015. <a href=\"https://doi.org/10.1093/aobpla/plv092\">https://doi.org/10.1093/aobpla/plv092</a>.","ieee":"S. Leuzinger, S. Fatichi, J. Cusens, C. Körner, and P. A. Niklaus, “The ‘island effect’ in terrestrial global change experiments: a problem with no solution?,” <i>AoB Plants</i>, vol. 7. Oxford University Press, 2015."},"day":"27","article_type":"original","extern":"1","publication":"AoB Plants","volume":7,"article_processing_charge":"No","type":"journal_article","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","author":[{"last_name":"Leuzinger","first_name":"Sebastian","full_name":"Leuzinger, Sebastian"},{"first_name":"Simone","last_name":"Fatichi","full_name":"Fatichi, Simone","id":"cf8e546b-a9b0-11f0-a43b-aa89ed1b56d6"},{"full_name":"Cusens, Jarrod","first_name":"Jarrod","last_name":"Cusens"},{"first_name":"Christian","last_name":"Körner","full_name":"Körner, Christian"},{"last_name":"Niklaus","first_name":"Pascal A.","full_name":"Niklaus, Pascal A."}],"title":"The ‘island effect’ in terrestrial global change experiments: a problem with no solution?","OA_place":"publisher","date_updated":"2026-08-12T08:09:20Z","das_tickbox":"1","oa_version":"Published Version"}]