On the convergence of random polynomials and multilinear forms

We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is equivalent to that of the multilinear form, and to the square summability of the c...

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Detalles Bibliográficos
Autores principales:	Carando, D., Dimant, V., Pinasco, D.
Formato:	JOUR
Materias:	Multilinear forms in random variables Polynomial Khintchine inequalities Polynomials in random variables
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00221236_v261_n8_p2135_Carando
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_00221236_v261_n8_p2135_Carando2023-10-03T14:27:15Z On the convergence of random polynomials and multilinear forms Carando, D. Dimant, V. Pinasco, D. Multilinear forms in random variables Polynomial Khintchine inequalities Polynomials in random variables We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is equivalent to that of the multilinear form, and to the square summability of the coefficients. Also, we present polynomial Khintchine inequalities for complex gaussian and Steinhaus variables. All these results have no analogues in the real case. Moreover, we study the Lp-convergence of random polynomials and derive certain decoupling inequalities without the usual tetrahedral hypothesis. We also consider convergence on "full subspaces" in the sense of Sjögren, both for real and complex random variables, and relate it to domination properties of the polynomial or the multilinear form, establishing a link with the theory of homogeneous polynomials on Banach spaces. © 2011 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221236_v261_n8_p2135_Carando
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Multilinear forms in random variables Polynomial Khintchine inequalities Polynomials in random variables
spellingShingle	Multilinear forms in random variables Polynomial Khintchine inequalities Polynomials in random variables Carando, D. Dimant, V. Pinasco, D. On the convergence of random polynomials and multilinear forms
topic_facet	Multilinear forms in random variables Polynomial Khintchine inequalities Polynomials in random variables
description	We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is equivalent to that of the multilinear form, and to the square summability of the coefficients. Also, we present polynomial Khintchine inequalities for complex gaussian and Steinhaus variables. All these results have no analogues in the real case. Moreover, we study the Lp-convergence of random polynomials and derive certain decoupling inequalities without the usual tetrahedral hypothesis. We also consider convergence on "full subspaces" in the sense of Sjögren, both for real and complex random variables, and relate it to domination properties of the polynomial or the multilinear form, establishing a link with the theory of homogeneous polynomials on Banach spaces. © 2011 Elsevier Inc.
format	JOUR
author	Carando, D. Dimant, V. Pinasco, D.
author_facet	Carando, D. Dimant, V. Pinasco, D.
author_sort	Carando, D.
title	On the convergence of random polynomials and multilinear forms
title_short	On the convergence of random polynomials and multilinear forms
title_full	On the convergence of random polynomials and multilinear forms
title_fullStr	On the convergence of random polynomials and multilinear forms
title_full_unstemmed	On the convergence of random polynomials and multilinear forms
title_sort	on the convergence of random polynomials and multilinear forms
url	http://hdl.handle.net/20.500.12110/paper_00221236_v261_n8_p2135_Carando
work_keys_str_mv	AT carandod ontheconvergenceofrandompolynomialsandmultilinearforms AT dimantv ontheconvergenceofrandompolynomialsandmultilinearforms AT pinascod ontheconvergenceofrandompolynomialsandmultilinearforms
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On the convergence of random polynomials and multilinear forms

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