An Erdös-Rényi law for nonconventional sums

Yuri Kifer

doi:10.1214/ECP.v20-4613

An Erdös-Rényi law for nonconventional sums

Yuri Kifer^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We obtain the Erdös-Rényi type law of large numbers for "nonconventional" sums of the form S _n =Σ ⁿ _m =1 F(X _m , X _2m ,…,X _ℓ _m ) where X ₁ ,X ₂ ,… is a sequence of i.i.d. random variables and F is a bounded Borel function. The proof relies on nonconventional large deviations obtained in [8].

Original language	English
Article number	83
Journal	Electronic Communications in Probability
Volume	20
DOIs	https://doi.org/10.1214/ECP.v20-4613
State	Published - 7 Nov 2015

Bibliographical note

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© 2015, University of Washington. All rights reserved.

Keywords

Large deviations
Laws of large numbers
Nonconventional setup

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10.1214/ECP.v20-4613

Cite this

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abstract = " We obtain the Erd{\"o}s-R{\'e}nyi type law of large numbers for {"}nonconventional{"} sums of the form S n =Σ n m =1 F(X m , X 2m ,…,X ℓ m ) where X 1 ,X 2 ,… is a sequence of i.i.d. random variables and F is a bounded Borel function. The proof relies on nonconventional large deviations obtained in [8].",

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AB - We obtain the Erdös-Rényi type law of large numbers for "nonconventional" sums of the form S n =Σ n m =1 F(X m , X 2m ,…,X ℓ m ) where X 1 ,X 2 ,… is a sequence of i.i.d. random variables and F is a bounded Borel function. The proof relies on nonconventional large deviations obtained in [8].

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KW - Nonconventional setup

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An Erdös-Rényi law for nonconventional sums

Abstract

Bibliographical note

Keywords

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