Differentiability of the diffusion coefficient for a family of intermittent maps
It is well known that the Liverani-Saussol-Vaienti map satisfies a central limit theorem for H\"older observables in the parameter regime where the correlations are summable. We show that when $C^2$ observables are considered, the variance of the limiting normal distribution is a $C^1$ function...
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| creator | Sélley, Fanni M |
| description | It is well known that the Liverani-Saussol-Vaienti map satisfies a central
limit theorem for H\"older observables in the parameter regime where the
correlations are summable. We show that when $C^2$ observables are considered,
the variance of the limiting normal distribution is a $C^1$ function of the
parameter. We first show this for the first return map to the base of the
second branch by studying the Green-Kubo formula, then conclude the result for
the original map using Kac's lemma and relying on linear response. |
| doi_str_mv | 10.48550/arxiv.2202.02048 |
| format | Article |
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limit theorem for H\"older observables in the parameter regime where the
correlations are summable. We show that when $C^2$ observables are considered,
the variance of the limiting normal distribution is a $C^1$ function of the
parameter. We first show this for the first return map to the base of the
second branch by studying the Green-Kubo formula, then conclude the result for
the original map using Kac's lemma and relying on linear response.</description><identifier>DOI: 10.48550/arxiv.2202.02048</identifier><language>eng</language><subject>Mathematics - Dynamical Systems</subject><creationdate>2022-02</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2202.02048$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2202.02048$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Sélley, Fanni M</creatorcontrib><title>Differentiability of the diffusion coefficient for a family of intermittent maps</title><description>It is well known that the Liverani-Saussol-Vaienti map satisfies a central
limit theorem for H\"older observables in the parameter regime where the
correlations are summable. We show that when $C^2$ observables are considered,
the variance of the limiting normal distribution is a $C^1$ function of the
parameter. We first show this for the first return map to the base of the
second branch by studying the Green-Kubo formula, then conclude the result for
the original map using Kac's lemma and relying on linear response.</description><subject>Mathematics - Dynamical Systems</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8lOwzAURb1hgQofwAr_QILjIbaXqIxSpbLoPrKd98STMlSOQfTvaQOruzhHVzqM3TWi1s4Y8RDyD33XUgpZCym0u2YfT4QIGaZCIdJA5cRn5OUTeH8GXwvNE08zIFKis8RxzjxwDCMNq0lTgTxSKRc4huNyw64wDAvc_u-GHV6eD9u3ard_fd8-7qrQWlepgN4IZXrvo9MpoW5No3sFjY8erDIqaBTRxgjGNg5aZz04cDJF2aveqg27_7tdk7pjpjHkU3dJ69Y09Qu3X0pI</recordid><startdate>20220204</startdate><enddate>20220204</enddate><creator>Sélley, Fanni M</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220204</creationdate><title>Differentiability of the diffusion coefficient for a family of intermittent maps</title><author>Sélley, Fanni M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-3af95035d99b84ccf46514d3e19b9e7353a4f0b7bbe5718e6879e8e82cb2d3d73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Dynamical Systems</topic><toplevel>online_resources</toplevel><creatorcontrib>Sélley, Fanni M</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Sélley, Fanni M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Differentiability of the diffusion coefficient for a family of intermittent maps</atitle><date>2022-02-04</date><risdate>2022</risdate><abstract>It is well known that the Liverani-Saussol-Vaienti map satisfies a central
limit theorem for H\"older observables in the parameter regime where the
correlations are summable. We show that when $C^2$ observables are considered,
the variance of the limiting normal distribution is a $C^1$ function of the
parameter. We first show this for the first return map to the base of the
second branch by studying the Green-Kubo formula, then conclude the result for
the original map using Kac's lemma and relying on linear response.</abstract><doi>10.48550/arxiv.2202.02048</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems |
| title | Differentiability of the diffusion coefficient for a family of intermittent maps |
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