# Tag Info

### What is the limit of $a (n + 1) / a (n)$?

The value is close to $e$ but not. It's actually the positive real root of $p(t) := t^3 - 2t^2 + t - 8$. This is solvable via ACSV (see book by Pemantle and Wilson 2013). To summarize, the ...
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Accepted

I don't think what you want is possible. In phase space $x$ and $v$ are basically quantities that can be independently prescribed. The first terms of your left hand side is linear in $v$. So fixing $... • 35.2k 3 votes ### Large deviation upper bound for Chi-squared random variable See B. Laurent and P.Massart, Adaptive estimation of a quadratic functional by model selection, Ann. Stat., 28 (2000) 1302--1338. Equations (4.3) and (4.4) say that for any$x\gt 0$: $$P(X_n \ge n + ... • 36.9k 3 votes Accepted ### Lower bound on the sum of pmf squared of a hypergeometric distribution Suppose that i=n-i=m (so that n=2m) and m is even; I suppose that such i and m you consider relevant. Then p_X(x)=\binom mx^2\Big/ \binom{2m}m\le\binom m{m/2}^2\Big/ \... • 110k 3 votes Accepted ### Complicated bound after using Stirling's approximation I understand from the reference to Stirling that you are looking for a large-d approximation of$$a_{\rm max}= \Bigl(\pi^{d/2}\Gamma(\frac{1}{2}d+1)^{-1} + 1\Bigr) \left(\frac{h^{d+1}}{2} \Gamma \... • 172k 3 votes ### Discrepancy bounds for moderate points counts in dimensions from d=2 to 32? As I understand it, you might be interested in a quantity called the inverse of the star-discrepancy. Given dimension$d$and some$\varepsilon > 0$, the inverse of the star-discrepancy$n(d,\...
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Let function $f : \mathbb R^{m \times n} \to \mathbb R_0^+$ be defined as follows f (\mathrm X) := \| \,\mathrm X \mathrm A^\top \|_\text{F}^2 + \| \,\mathrm X^\top \mathrm A \,\|_\text{F}^2 + \...