{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T15:50:05Z","timestamp":1776095405154,"version":"3.50.1"},"reference-count":31,"publisher":"American Mathematical Society (AMS)","issue":"11","license":[{"start":{"date-parts":[[2015,11,10]],"date-time":"2015-11-10T00:00:00Z","timestamp":1447113600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Trans. Amer. Math. Soc."],"abstract":"<p>\n                    The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non-periodic points. Then we build a general theory of Extreme Value Laws for randomly perturbed dynamical systems. We also address, in both situations, the convergence of Rare Events Point Processes. Decay of correlations against\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L Superscript 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    observables will play a central role in our investigations.\n                  <\/p>","DOI":"10.1090\/s0002-9947-2014-06300-9","type":"journal-article","created":{"date-parts":[[2014,11,10]],"date-time":"2014-11-10T14:17:55Z","timestamp":1415629075000},"page":"8229-8278","source":"Crossref","is-referenced-by-count":42,"special_numbering":"966","title":["Laws of rare events for deterministic and random dynamical systems"],"prefix":"10.1090","volume":"367","author":[{"given":"Hale","family":"Ayta\u00e7","sequence":"first","affiliation":[]},{"given":"Jorge","family":"Freitas","sequence":"additional","affiliation":[]},{"given":"Sandro","family":"Vaienti","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2014,11,10]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"1203","DOI":"10.1016\/j.aim.2011.06.014","article-title":"From rates of mixing to recurrence times via large deviations","volume":"228","author":"Alves, Jos\u00e9 F.","year":"2011","journal-title":"Adv. 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