000107385 001__ 107385
000107385 005__ 20230519145348.0
000107385 0247_ $$2doi$$a10.1016/j.jfa.2020.108779
000107385 0248_ $$2sideral$$a120103
000107385 037__ $$aART-2021-120103
000107385 041__ $$aeng
000107385 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso Gutiérrez, David$$uUniversidad de Zaragoza
000107385 245__ $$aLarge deviations, moderate deviations, and the KLS conjecture
000107385 260__ $$c2021
000107385 5060_ $$aAccess copy available to the general public$$fUnrestricted
000107385 5203_ $$aHaving its origin in theoretical computer science, the Kannan-Lov\'asz-Simonovits (KLS) conjecture is one of the major open problems in asymptotic convex geometry and high-dimensional probability theory today. In this work, we establish a connection between this conjecture and the study of large and moderate deviations for isotropic log-concave random vectors. We then study the moderate deviations for the Euclidean norm of random orthogonally projected random vectors in an $\ell_p^n$--ball. This leads to a number of interesting observations: (A) the $\ell_1^n$--ball is critical for the new approach; (B) for $p\geq 2$ the rate function in the moderate deviations principle undergoes a phase transition, depending on whether the scaling is below the square-root of the subspace dimensions or comparable; (C) for $1\leq p<2$ and comparable subspace dimensions, the rate function again displays a phase transition depending on its growth relative to n^{p/2}.
000107385 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48-20R$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-P$$9info:eu-repo/grantAgreement/ES/MICINN/PID2019-105979GP-I00
000107385 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000107385 590__ $$a1.891$$b2021
000107385 592__ $$a1.819$$b2021
000107385 594__ $$a2.7$$b2021
000107385 591__ $$aMATHEMATICS$$b47 / 333 = 0.141$$c2021$$dQ1$$eT1
000107385 593__ $$aAnalysis$$c2021$$dQ1
000107385 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000107385 700__ $$aProchno, Joscha
000107385 700__ $$aThäle, Christoph
000107385 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático
000107385 773__ $$g280, 1 (2021), 108779 1-33$$pJ. funct. anal.$$tJOURNAL OF FUNCTIONAL ANALYSIS$$x0022-1236
000107385 8564_ $$s458041$$uhttps://zaguan.unizar.es/record/107385/files/texto_completo.pdf$$yPostprint
000107385 8564_ $$s2303411$$uhttps://zaguan.unizar.es/record/107385/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000107385 909CO $$ooai:zaguan.unizar.es:107385$$particulos$$pdriver
000107385 951__ $$a2023-05-18-13:23:36
000107385 980__ $$aARTICLE