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LSpice
LSpice
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random Random probability following a log concave distribution of order p

In the article "Concentration of the information in data with Log-concave distributions""Concentration of the information in data with Log-concave distributions" of Bobkov and Madiman, it is written thethat if $X$ is a positive random variable following a log concave distribution of order p$p$, then one has $V(X) \leq \frac{E(X)^2}{p}$. A reference is given, but I don't understand how the result follows from the reference. Also, it seems quite hard to prove, and the problem where those variables came from is said to be "easy" (it's the one dimension optimal matching problem), so I start to feel like I have misunderstood something.

Have you seen this inequality? Is it possible to give a relatively short proof?

random probability following a log concave distribution of order p

In the article "Concentration of the information in data with Log-concave distributions" of Bobkov and Madiman, it is written the if $X$ is a positive random variable following a log concave distribution of order p, then one has $V(X) \leq \frac{E(X)^2}{p}$ A reference is given, but I don't understand how the result follows from the reference. Also, it seems quite hard to prove, and the problem where those variables came from is said to be "easy" (it's the one dimension optimal matching problem), so I start to feel like I have misunderstood something.

Have you seen this inequality? Is it possible to give a relatively short proof?

Random probability following a log concave distribution of order p

In the article "Concentration of the information in data with Log-concave distributions" of Bobkov and Madiman, it is written that if $X$ is a positive random variable following a log concave distribution of order $p$, then one has $V(X) \leq \frac{E(X)^2}{p}$. A reference is given, but I don't understand how the result follows from the reference. Also, it seems quite hard to prove, and the problem where those variables came from is said to be "easy" (it's the one dimension optimal matching problem), so I start to feel like I have misunderstood something.

Have you seen this inequality? Is it possible to give a relatively short proof?

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Glorfindel
Glorfindel
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In the article "CONCENTRATION OF THE INFORMATION IN DATA WITH"Concentration of the information in data with LOGLog-CONCAVE DISTRIBUTIONS"concave distributions" of Bobkov and Madiman, it is written the if $X$ is a positive random variable following a log concave distribution of order p, then one has $V(X) \leq \frac{E(X)^2}{p}$ A reference sis given, but I don't understand how the resulatresult follows from the reference. Also, it seems quite hard to prove, and the problem where thoosethose variables came from is said to be "easy" (it's the one dimension optimal matching problem), so I start to feel like I have issunderstoodmisunderstood something.

haveHave you seen this inequality  ? Is it possible to give a relatively short proof  ?

In the article "CONCENTRATION OF THE INFORMATION IN DATA WITH LOG-CONCAVE DISTRIBUTIONS" of Bobkov and Madiman, it is written the if $X$ is a positive random variable following a log concave distribution of order p, then one has $V(X) \leq \frac{E(X)^2}{p}$ A reference s given, but I don't understand how the resulat follows from the reference. Also, it seems quite hard to prove, and the problem where thoose variables came from is said to be "easy" (it's the one dimension optimal matching problem), so I start to feel like I have issunderstood something.

have you seen this inequality  ? Is it possible to give a relatively short proof  ?

In the article "Concentration of the information in data with Log-concave distributions" of Bobkov and Madiman, it is written the if $X$ is a positive random variable following a log concave distribution of order p, then one has $V(X) \leq \frac{E(X)^2}{p}$ A reference is given, but I don't understand how the result follows from the reference. Also, it seems quite hard to prove, and the problem where those variables came from is said to be "easy" (it's the one dimension optimal matching problem), so I start to feel like I have misunderstood something.

Have you seen this inequality? Is it possible to give a relatively short proof?

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Enguerrand Moulinier
Enguerrand Moulinier
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random probability following a log concave distribution of order p

In the article "CONCENTRATION OF THE INFORMATION IN DATA WITH LOG-CONCAVE DISTRIBUTIONS" of Bobkov and Madiman, it is written the if $X$ is a positive random variable following a log concave distribution of order p, then one has $V(X) \leq \frac{E(X)^2}{p}$ A reference s given, but I don't understand how the resulat follows from the reference. Also, it seems quite hard to prove, and the problem where thoose variables came from is said to be "easy" (it's the one dimension optimal matching problem), so I start to feel like I have issunderstood something.

have you seen this inequality ? Is it possible to give a relatively short proof ?