78917 20200117213750.0 doi 10.1016/j.aam.2018.04.003 sideral 105388 ART-2018-105388 eng (orcid)0000-0003-1256-3671 Alonso Gutiérrez, David Universidad de Zaragoza Large deviations for high-dimensional random projections of l_p^n balls 2018 Access copy available to the general public Unrestricted The paper provides a description of the large deviation behavior for the Euclidean norm of projections of View the MathML sourcelpn-balls to high-dimensional random subspaces. More precisely, for each integer n=1n=1, let kn¿{1,…,n-1}kn¿{1,…,n-1}, E(n)E(n) be a uniform random knkn-dimensional subspace of RnRn and X(n)X(n) be a random point that is uniformly distributed in the View the MathML sourcelpn-ball of RnRn for some p¿[1,8]p¿[1,8]. Then the Euclidean norms ¿PE(n)X(n)¿2¿PE(n)X(n)¿2 of the orthogonal projections are shown to satisfy a large deviation principle as the space dimension n tends to infinity. Its speed and rate function are identified, making thereby visible how they depend on p and the growth of the sequence of subspace dimensions knkn. As a key tool we prove a probabilistic representation of ¿PE(n)X(n)¿2¿PE(n)X(n)¿2 which allows us to separate the influence of the parameter p and the subspace dimension knkn. info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.008 2018 MATHEMATICS, APPLIED 141 / 254 = 0.555 2018 Q3 T2 0.688 2018 Applied Mathematics 2018 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Prochno, Joscha Thäle, Christoph 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 99 (2018), 1-35 Adv. appl. math. ADVANCES IN APPLIED MATHEMATICS 0196-8858 495566 http://zaguan.unizar.es/record/78917/files/texto_completo.pdf Postprint 42624 http://zaguan.unizar.es/record/78917/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:78917 articulos driver 2020-01-17-21:31:46 ARTICLE