User leonbloy - MathOverflow

Answer by leonbloy for 2d moment of chebyshev

2011-12-02T14:19:29Z

If you are interested in approximation for large $n,d$, with a simple Poissonization argument I get:

$$ E(X^{2d}) \approx n^{2d} \left( \frac{1+e^{-2\lambda}}{2} \right)^n$$

where $\lambda = \frac{2d}{n}$

Answer by leonbloy for Proofs without words

2011-06-28T14:42:08Z

(I'd post this as a comment to Mariano Suárez-Alvarez, but I've not enough rep). From a ME thread.

$$\sum_{k=1}^n (-1)^{n-k} k^2 = {n+1 \choose 2} = \sum_{k=1}^n \; k = \frac{(n+1) \; n}{2}$$

Answer by leonbloy for Probability of a Random Walk crossing a straight line

2011-05-10T01:42:27Z

(Just a hint. Should be a comment more than an answer, but don't have enough rep)

It seems interesting the slightly more general problem in which the initial distance to the line is greater than zero - or that the line has the equation $a n + b$ Considering $a$ fixed and $b$ variable, one can get (if I'm not mistaken) a the following equation on $P(b)$ (probability that the process crosses the line) as:

$P(b)= \left\{ \begin{array}{ll} \frac{1}{2}\left[ P(b+a-1)+P(b+a+1) \right] & \mbox{if } b \geq 0 \\ 1 & \mbox{if } b < 0 \end{array} \right. $

We want a solution (apart from the trivial $P(b)=1$) that goes to zero as $b \to \infty$ , and we are specially interested in $P(0^+)$ Does not seem easy, seems very sensitive to the parameter $a$. I believe that if $a$ is rational, $a=m/n$, the funcion has discontinuites at points $k/n$.

Answer by leonbloy for Examples of common false beliefs in mathematics.

2011-05-09T20:05:37Z

"Suppose that two features $[x,y]$ from a population $P$ are positively correlated, and we divide $P$ into two subclasses $P_1$, $P_2$. Then, it cannot happen that the respective features ( $[x_1,y1]$ and $[x_2,y_2]$) are negatively correlated in both subclasses

Or more succintly:

"Mixing preserves the correlation sign."

This seems very plausible - almost obvious. But it's false - see Simpon's paradox

Answer by leonbloy for duplicate detection problem

2010-05-20T20:54:27Z

Basically David's approach: we fix $M$ = number of bits storage, and compute the indicator $ h = XOR ( hash_M (a [i] ) ) $

where $hash_M$ is a hash function to $M$ bits (eg MD5 masked to M bits). We decide that it is a permutation without repetitions by comparing with the same indicator for the ordered array (1..N). This is order N. And there is a probability of error which should be around $1/2^M$... if I'm not mistaken.

Comment by leonbloy

2012-12-19T15:59:00Z

Another heuristic to adapt the "fit polygon" problem to the "fit points" recipe would be to insert equispaced phantom points along the poygon sides.