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Quantities of interest are the number of servers that receive the information before the capital of all the informed servers is exhausted and the exhaustion time. We establish limit theorems (law of large numbers, central limit theorem and large deviation principle), as <jats:italic>n<\/jats:italic> \u2192 \u221e, for the proportion of informed vertices before exhaustion and for the total duration. The analysis relies on a construction of the transmission procedure as a dynamical selection of successful nodes in a Galton\u2013Watson tree with respect to the success epochs of the coupon collector problem.<\/jats:p>","DOI":"10.1017\/s096354831400039x","type":"journal-article","created":{"date-parts":[[2014,9,4]],"date-time":"2014-09-04T23:59:40Z","timestamp":1409875180000},"page":"973-1009","source":"Crossref","is-referenced-by-count":8,"title":["Information Transmission under Random Emission Constraints"],"prefix":"10.1017","volume":"23","author":[{"given":"FRANCIS","family":"COMETS","sequence":"first","affiliation":[]},{"given":"FRAN\u00c7OIS","family":"DELARUE","sequence":"additional","affiliation":[]},{"given":"REN\u00c9","family":"SCHOTT","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,9,4]]},"reference":[{"key":"S096354831400039X_ref24","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177699266"},{"key":"S096354831400039X_ref22","doi-asserted-by":"publisher","DOI":"10.1214\/009117905000000413"},{"key":"S096354831400039X_ref6","volume-title":"Convergence of Probability Measures","author":"Billingsley","year":"1968"},{"key":"S096354831400039X_ref27","first-page":"209","article-title":"CLT for the proportion of infected individuals for an epidemic model on a complete graph","volume":"17","author":"Machado","year":"2011","journal-title":"Markov Proc. 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