ψα-ESTIMATES FOR MARGINALS OF LOG-CONCAVE PROBABILITY MEASURES
We show that a random marginal πF (μ) of an isotropie log-concave probability measure μ on ℝ n exhibits better ψ α -behavior. For a natural variant ψ' α of the standard ψ α -norm we show the following: (i) If $k \le \sqrt n $ , then for a random F ∊ G n,k we have that πF(μ) is a ψ'₂-measur...
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2012-04, Vol.140 (4), p.1297-1308 |
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| creator | GIANNOPOULOS, A. PAOURIS, G. VALETTAS, P. |
| description | We show that a random marginal πF (μ) of an isotropie log-concave probability measure μ on ℝ n exhibits better ψ α -behavior. For a natural variant ψ' α of the standard ψ α -norm we show the following: (i) If $k \le \sqrt n $ , then for a random F ∊ G n,k we have that πF(μ) is a ψ'₂-measure. We complement this result by showing that a random πF(μ) is, at the same time, super-Gaussian. (ii) If k = n δ , ½ < δ < 1, then for a random F ∊ G n,k we have that πF(μ) is a ψ' α(δ) -measure, where $\[\alpha \left( \delta \right) = \frac{{2\delta }}{{3\delta - 1}}]$ . |
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For a natural variant ψ' α of the standard ψ α -norm we show the following: (i) If $k \le \sqrt n $ , then for a random F ∊ G n,k we have that πF(μ) is a ψ'₂-measure. We complement this result by showing that a random πF(μ) is, at the same time, super-Gaussian. (ii) If k = n δ , ½ < δ < 1, then for a random F ∊ G n,k we have that πF(μ) is a ψ' α(δ) -measure, where $\[\alpha \left( \delta \right) = \frac{{2\delta }}{{3\delta - 1}}]$ .</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><language>eng</language><publisher>American Mathematical Society</publisher><subject>Asymptotic theory ; Central limit theorem ; College mathematics ; Density ; Functional analysis ; Mathematical constants ; Mathematical functions ; Mathematical inequalities ; Mathematical theorems</subject><ispartof>Proceedings of the American Mathematical Society, 2012-04, Vol.140 (4), p.1297-1308</ispartof><rights>2012 American Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/41505582$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/41505582$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>GIANNOPOULOS, A.</creatorcontrib><creatorcontrib>PAOURIS, G.</creatorcontrib><creatorcontrib>VALETTAS, P.</creatorcontrib><title>ψα-ESTIMATES FOR MARGINALS OF LOG-CONCAVE PROBABILITY MEASURES</title><title>Proceedings of the American Mathematical Society</title><description>We show that a random marginal πF (μ) of an isotropie log-concave probability measure μ on ℝ n exhibits better ψ α -behavior. 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(ii) If k = n δ , ½ < δ < 1, then for a random F ∊ G n,k we have that πF(μ) is a ψ' α(δ) -measure, where $\[\alpha \left( \delta \right) = \frac{{2\delta }}{{3\delta - 1}}]$ .</description><subject>Asymptotic theory</subject><subject>Central limit theorem</subject><subject>College mathematics</subject><subject>Density</subject><subject>Functional analysis</subject><subject>Mathematical constants</subject><subject>Mathematical functions</subject><subject>Mathematical inequalities</subject><subject>Mathematical theorems</subject><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpjYuA0NLCw0DWzMDJjYeA0MDAw0rW0NLbkYOAqLs4Ccg0tTcw5GRzOd5zbqOsaHOLp6xjiGqzg5h-k4OsY5O7p5-gTrODvpuDj767r7O_n7BjmqhAQ5O_k6OTp4xkSqeDr6hgcGuQazMPAmpaYU5zKC6W5GWTdXEOcPXSzikvyi-ILijJzE4sq400MTQ1MTS2MjAnJAwCIgjFL</recordid><startdate>20120401</startdate><enddate>20120401</enddate><creator>GIANNOPOULOS, A.</creator><creator>PAOURIS, G.</creator><creator>VALETTAS, P.</creator><general>American Mathematical Society</general><scope/></search><sort><creationdate>20120401</creationdate><title>ψα-ESTIMATES FOR MARGINALS OF LOG-CONCAVE PROBABILITY MEASURES</title><author>GIANNOPOULOS, A. ; PAOURIS, G. ; VALETTAS, P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-jstor_primary_415055823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Asymptotic theory</topic><topic>Central limit theorem</topic><topic>College mathematics</topic><topic>Density</topic><topic>Functional analysis</topic><topic>Mathematical constants</topic><topic>Mathematical functions</topic><topic>Mathematical inequalities</topic><topic>Mathematical theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>GIANNOPOULOS, A.</creatorcontrib><creatorcontrib>PAOURIS, G.</creatorcontrib><creatorcontrib>VALETTAS, P.</creatorcontrib><jtitle>Proceedings of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>GIANNOPOULOS, A.</au><au>PAOURIS, G.</au><au>VALETTAS, P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ψα-ESTIMATES FOR MARGINALS OF LOG-CONCAVE PROBABILITY MEASURES</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><date>2012-04-01</date><risdate>2012</risdate><volume>140</volume><issue>4</issue><spage>1297</spage><epage>1308</epage><pages>1297-1308</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><abstract>We show that a random marginal πF (μ) of an isotropie log-concave probability measure μ on ℝ n exhibits better ψ α -behavior. For a natural variant ψ' α of the standard ψ α -norm we show the following: (i) If $k \le \sqrt n $ , then for a random F ∊ G n,k we have that πF(μ) is a ψ'₂-measure. We complement this result by showing that a random πF(μ) is, at the same time, super-Gaussian. (ii) If k = n δ , ½ < δ < 1, then for a random F ∊ G n,k we have that πF(μ) is a ψ' α(δ) -measure, where $\[\alpha \left( \delta \right) = \frac{{2\delta }}{{3\delta - 1}}]$ .</abstract><pub>American Mathematical Society</pub></addata></record> |
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| source | Jstor Complete Legacy; American Mathematical Society Publications; American Mathematical Society Publications (Freely Accessible); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics |
| subjects | Asymptotic theory Central limit theorem College mathematics Density Functional analysis Mathematical constants Mathematical functions Mathematical inequalities Mathematical theorems |
| title | ψα-ESTIMATES FOR MARGINALS OF LOG-CONCAVE PROBABILITY MEASURES |
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