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000078917 005__ 20200117213750.0
000078917 0247_ $$2doi$$a10.1016/j.aam.2018.04.003
000078917 0248_ $$2sideral$$a105388
000078917 037__ $$aART-2018-105388
000078917 041__ $$aeng
000078917 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso Gutiérrez, David$$uUniversidad de Zaragoza
000078917 245__ $$aLarge deviations for high-dimensional random projections of l_p^n balls
000078917 260__ $$c2018
000078917 5060_ $$aAccess copy available to the general public$$fUnrestricted
000078917 5203_ $$aThe 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.
000078917 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-P
000078917 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000078917 590__ $$a1.008$$b2018
000078917 591__ $$aMATHEMATICS, APPLIED$$b141 / 254 = 0.555$$c2018$$dQ3$$eT2
000078917 592__ $$a0.688$$b2018
000078917 593__ $$aApplied Mathematics$$c2018$$dQ2
000078917 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000078917 700__ $$aProchno, Joscha
000078917 700__ $$aThäle, Christoph
000078917 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000078917 773__ $$g99 (2018), 1-35$$pAdv. appl. math.$$tADVANCES IN APPLIED MATHEMATICS$$x0196-8858
000078917 8564_ $$s495566$$uhttps://zaguan.unizar.es/record/78917/files/texto_completo.pdf$$yPostprint
000078917 8564_ $$s42624$$uhttps://zaguan.unizar.es/record/78917/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000078917 909CO $$ooai:zaguan.unizar.es:78917$$particulos$$pdriver
000078917 951__ $$a2020-01-17-21:31:46
000078917 980__ $$aARTICLE