7
$\begingroup$

A sequence $(a_n)$ is said to be log-concave provided $a_i^2 \geq a_{i-1}a_{i+1}$ for all $i$.

What sorts of intuition can one have about log-concave sequences? In particular, what kind of "picture" does the property of log-concavity conjure up with regard to its graph?

What nice things happen when a sequence is log-concave? What are typical "next steps" after one has established the log-concavity of a sequence?

Any other comments related to getting a feel for log-concave sequences are most welcome.

$\endgroup$
1
$\begingroup$

As for nice properties of log-concave functions, there are many applications in probability. For example, if the PDF of a function is log-concave, so is the CDF.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.