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for questions involving inequalities, upper and lower bounds.
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1
answer
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upper bound involving recursions
Suppose that I have the following recursion for all $a_k >1$: $a_{k+1}^2 \leq a_k^2 - a_k$. Then one can see that the following inequality is true (proved via induction): $a_k \leq a_0 - \frac{k}{2}$. …
2
votes
1
answer
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Log-Sobolev constant
Let $\nu \propto e^{-f}$ be a probability density on $\mathbb{R}^d$ with full support. We say $\nu$ satisfies the log-Sobolev inequality (LSI) with constant $\alpha$ if for every smooth function $g:\m …