Loading…
Berry–Esseen Bounds with Targets and Local Limit Theorems for Products of Random Matrices
Let μ be a probability measure on GL d ( R ) and denote by S n : = g n ⋯ g 1 the associated random matrix product, where g j ’s are i.i.d.’s with law μ . We study statistical properties of random variables of the form σ ( S n , x ) + u ( S n x ) , where x ∈ P d - 1 , σ is the norm cocycle and u belo...
Saved in:
| Published in: | The Journal of geometric analysis 2023-03, Vol.33 (3), Article 76 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c358t-9695660b9b85f429771af33dbb655036d0151310e6562f5c41ea79036ee3ad303 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c358t-9695660b9b85f429771af33dbb655036d0151310e6562f5c41ea79036ee3ad303 |
| container_end_page | |
| container_issue | 3 |
| container_start_page | |
| container_title | The Journal of geometric analysis |
| container_volume | 33 |
| creator | Dinh, Tien-Cuong Kaufmann, Lucas Wu, Hao |
| description | Let
μ
be a probability measure on
GL
d
(
R
)
and denote by
S
n
:
=
g
n
⋯
g
1
the associated random matrix product, where
g
j
’s are i.i.d.’s with law
μ
. We study statistical properties of random variables of the form
σ
(
S
n
,
x
)
+
u
(
S
n
x
)
,
where
x
∈
P
d
-
1
,
σ
is the norm cocycle and
u
belongs to a class of admissible functions on
P
d
-
1
with values in
R
∪
{
±
∞
}
. Assuming that
μ
has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we obtain optimal Berry–Esseen bounds and the Local Limit Theorem for such variables using a large class of observables on
R
and Hölder continuous target functions on
P
d
-
1
. As particular cases, we obtain new limit theorems for
σ
(
S
n
,
x
)
and for the coefficients of
S
n
. |
| doi_str_mv | 10.1007/s12220-022-01127-3 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2762939864</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2762939864</sourcerecordid><originalsourceid>FETCH-LOGICAL-c358t-9695660b9b85f429771af33dbb655036d0151310e6562f5c41ea79036ee3ad303</originalsourceid><addsrcrecordid>eNp9kN9KwzAUh4MoOKcv4FXA6-hJ0qTLpRvzD1QUmSB4EdI23TrWZiYtsjvfwTf0SYxW8M6rc-B8v9-BD6FTCucUIL0IlDEGBBgjQClLCd9DIyqEIgDseT_uIIBIxeQhOgphDZBInqQj9DK13u8-3z_mIVjb4qnr2zLgt7pb4YXxS9sFbNoSZ64wG5zVTd3hxco6b5uAK-fxg3dlX0TKVfgxkq7Bd6bzdWHDMTqozCbYk985Rk9X88XshmT317ezy4wUXEw6oqQSUkKu8omoEqbSlJqK8zLPpRDAZQlUUE7BSiFZJYqEWpOqeLCWm5IDH6OzoXfr3WtvQ6fXrvdtfKlZKpniaiKTSLGBKrwLwdtKb33dGL_TFPS3RD1I1FGi_pGoeQzxIRQi3C6t_6v-J_UFolx0GA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2762939864</pqid></control><display><type>article</type><title>Berry–Esseen Bounds with Targets and Local Limit Theorems for Products of Random Matrices</title><source>Springer Nature</source><creator>Dinh, Tien-Cuong ; Kaufmann, Lucas ; Wu, Hao</creator><creatorcontrib>Dinh, Tien-Cuong ; Kaufmann, Lucas ; Wu, Hao</creatorcontrib><description>Let
μ
be a probability measure on
GL
d
(
R
)
and denote by
S
n
:
=
g
n
⋯
g
1
the associated random matrix product, where
g
j
’s are i.i.d.’s with law
μ
. We study statistical properties of random variables of the form
σ
(
S
n
,
x
)
+
u
(
S
n
x
)
,
where
x
∈
P
d
-
1
,
σ
is the norm cocycle and
u
belongs to a class of admissible functions on
P
d
-
1
with values in
R
∪
{
±
∞
}
. Assuming that
μ
has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we obtain optimal Berry–Esseen bounds and the Local Limit Theorem for such variables using a large class of observables on
R
and Hölder continuous target functions on
P
d
-
1
. As particular cases, we obtain new limit theorems for
σ
(
S
n
,
x
)
and for the coefficients of
S
n
.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-022-01127-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Continuity (mathematics) ; Convex and Discrete Geometry ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Mathematics ; Mathematics and Statistics ; Nessim Sibony: In Memoriam ; Random variables ; Statistical analysis ; Theorems</subject><ispartof>The Journal of geometric analysis, 2023-03, Vol.33 (3), Article 76</ispartof><rights>Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-9695660b9b85f429771af33dbb655036d0151310e6562f5c41ea79036ee3ad303</citedby><cites>FETCH-LOGICAL-c358t-9695660b9b85f429771af33dbb655036d0151310e6562f5c41ea79036ee3ad303</cites><orcidid>0000-0001-9043-4862</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Dinh, Tien-Cuong</creatorcontrib><creatorcontrib>Kaufmann, Lucas</creatorcontrib><creatorcontrib>Wu, Hao</creatorcontrib><title>Berry–Esseen Bounds with Targets and Local Limit Theorems for Products of Random Matrices</title><title>The Journal of geometric analysis</title><addtitle>J Geom Anal</addtitle><description>Let
μ
be a probability measure on
GL
d
(
R
)
and denote by
S
n
:
=
g
n
⋯
g
1
the associated random matrix product, where
g
j
’s are i.i.d.’s with law
μ
. We study statistical properties of random variables of the form
σ
(
S
n
,
x
)
+
u
(
S
n
x
)
,
where
x
∈
P
d
-
1
,
σ
is the norm cocycle and
u
belongs to a class of admissible functions on
P
d
-
1
with values in
R
∪
{
±
∞
}
. Assuming that
μ
has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we obtain optimal Berry–Esseen bounds and the Local Limit Theorem for such variables using a large class of observables on
R
and Hölder continuous target functions on
P
d
-
1
. As particular cases, we obtain new limit theorems for
σ
(
S
n
,
x
)
and for the coefficients of
S
n
.</description><subject>Abstract Harmonic Analysis</subject><subject>Continuity (mathematics)</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nessim Sibony: In Memoriam</subject><subject>Random variables</subject><subject>Statistical analysis</subject><subject>Theorems</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kN9KwzAUh4MoOKcv4FXA6-hJ0qTLpRvzD1QUmSB4EdI23TrWZiYtsjvfwTf0SYxW8M6rc-B8v9-BD6FTCucUIL0IlDEGBBgjQClLCd9DIyqEIgDseT_uIIBIxeQhOgphDZBInqQj9DK13u8-3z_mIVjb4qnr2zLgt7pb4YXxS9sFbNoSZ64wG5zVTd3hxco6b5uAK-fxg3dlX0TKVfgxkq7Bd6bzdWHDMTqozCbYk985Rk9X88XshmT317ezy4wUXEw6oqQSUkKu8omoEqbSlJqK8zLPpRDAZQlUUE7BSiFZJYqEWpOqeLCWm5IDH6OzoXfr3WtvQ6fXrvdtfKlZKpniaiKTSLGBKrwLwdtKb33dGL_TFPS3RD1I1FGi_pGoeQzxIRQi3C6t_6v-J_UFolx0GA</recordid><startdate>20230301</startdate><enddate>20230301</enddate><creator>Dinh, Tien-Cuong</creator><creator>Kaufmann, Lucas</creator><creator>Wu, Hao</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9043-4862</orcidid></search><sort><creationdate>20230301</creationdate><title>Berry–Esseen Bounds with Targets and Local Limit Theorems for Products of Random Matrices</title><author>Dinh, Tien-Cuong ; Kaufmann, Lucas ; Wu, Hao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-9695660b9b85f429771af33dbb655036d0151310e6562f5c41ea79036ee3ad303</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Continuity (mathematics)</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nessim Sibony: In Memoriam</topic><topic>Random variables</topic><topic>Statistical analysis</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dinh, Tien-Cuong</creatorcontrib><creatorcontrib>Kaufmann, Lucas</creatorcontrib><creatorcontrib>Wu, Hao</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of geometric analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dinh, Tien-Cuong</au><au>Kaufmann, Lucas</au><au>Wu, Hao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Berry–Esseen Bounds with Targets and Local Limit Theorems for Products of Random Matrices</atitle><jtitle>The Journal of geometric analysis</jtitle><stitle>J Geom Anal</stitle><date>2023-03-01</date><risdate>2023</risdate><volume>33</volume><issue>3</issue><artnum>76</artnum><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>Let
μ
be a probability measure on
GL
d
(
R
)
and denote by
S
n
:
=
g
n
⋯
g
1
the associated random matrix product, where
g
j
’s are i.i.d.’s with law
μ
. We study statistical properties of random variables of the form
σ
(
S
n
,
x
)
+
u
(
S
n
x
)
,
where
x
∈
P
d
-
1
,
σ
is the norm cocycle and
u
belongs to a class of admissible functions on
P
d
-
1
with values in
R
∪
{
±
∞
}
. Assuming that
μ
has a finite exponential moment and generates a proximal and strongly irreducible semigroup, we obtain optimal Berry–Esseen bounds and the Local Limit Theorem for such variables using a large class of observables on
R
and Hölder continuous target functions on
P
d
-
1
. As particular cases, we obtain new limit theorems for
σ
(
S
n
,
x
)
and for the coefficients of
S
n
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-022-01127-3</doi><orcidid>https://orcid.org/0000-0001-9043-4862</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1050-6926 |
| ispartof | The Journal of geometric analysis, 2023-03, Vol.33 (3), Article 76 |
| issn | 1050-6926 1559-002X |
| language | eng |
| recordid | cdi_proquest_journals_2762939864 |
| source | Springer Nature |
| subjects | Abstract Harmonic Analysis Continuity (mathematics) Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Nessim Sibony: In Memoriam Random variables Statistical analysis Theorems |
| title | Berry–Esseen Bounds with Targets and Local Limit Theorems for Products of Random Matrices |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T23%3A54%3A42IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Berry%E2%80%93Esseen%20Bounds%20with%20Targets%20and%20Local%20Limit%20Theorems%20for%20Products%20of%20Random%20Matrices&rft.jtitle=The%20Journal%20of%20geometric%20analysis&rft.au=Dinh,%20Tien-Cuong&rft.date=2023-03-01&rft.volume=33&rft.issue=3&rft.artnum=76&rft.issn=1050-6926&rft.eissn=1559-002X&rft_id=info:doi/10.1007/s12220-022-01127-3&rft_dat=%3Cproquest_cross%3E2762939864%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c358t-9695660b9b85f429771af33dbb655036d0151310e6562f5c41ea79036ee3ad303%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2762939864&rft_id=info:pmid/&rfr_iscdi=true |