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Rotatable random sequences in local fields Evans, Steve
Description
An infinite sequence of real random variables $(\xi_1, \xi_2, \ldots)$ is said to be rotatable if every finite subsequence $(\xi_1, \ldots, \xi_n)$ has a spherically symmetric distribution. A classical theorem of David Freedman says that $(\xi_1, \xi_2, \ldots)$ is rotatable if and only if $\xi_j = \sigma \eta_j$ for all $j$, where $(\eta_1, \eta_2, \ldots)$ is a sequence of independent standard Gaussian random variables and $\sigma$ is an independent nonnegative random variable. We establish the analogue of Freedman's result for sequences of random variables taking values in arbitrary locally compact, nondiscrete fields other than the field of real numbers or the field of complex numbers. This is joint work with Daniel Raban, a Berkeley undergraduate.
Item Metadata
Title |
Rotatable random sequences in local fields
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-10-23T15:30
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Description |
An infinite sequence of real random variables $(\xi_1,
\xi_2, \ldots)$ is said to be rotatable if every finite subsequence
$(\xi_1, \ldots, \xi_n)$ has a spherically
symmetric distribution. A classical theorem of David Freedman says
that $(\xi_1, \xi_2, \ldots)$ is rotatable if and only if $\xi_j =
\sigma \eta_j$ for all $j$, where $(\eta_1, \eta_2, \ldots)$ is a
sequence of independent standard Gaussian random variables and
$\sigma$ is an independent nonnegative random variable. We establish
the analogue of Freedman's result for sequences of random variables
taking values in arbitrary locally compact, nondiscrete fields other
than the field of real numbers or the field of complex numbers. This
is joint work with Daniel Raban, a Berkeley undergraduate.
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Extent |
45 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of California, Berkeley
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Series | |
Date Available |
2018-04-22
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0365950
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International