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My second comment indicates that I think you need to amend your conjecture, or else I don't understand. Allow me to sketch some relevant ideas for getting non-trivial lower bounds. If my sketch do …

Problem instance: A closed convex body $B\subset {\Bbb R}^n$ of volume 1; a point $p\in B$; and a real number $v\in(0,1)$. Objective: Find the probability $P(B,v,p)$ that $p\in B'$, for $B'$ a random …

I previously asked generally what people knew or conjectured concerning the moments of the probability distribution governing $M_n:= g_n/\ln(p_n)$, the normalized $n$th prime gap (or ``merit''). Greg …

The Probabilistic Method by Noga Alon and Joel Spencer! Not a probability textbook per se ---Feller or whatever for that--- but sufficiently self-contained that one can learn the tools as one sees t …

This story yesterday (no need to follow the link to understand the question!) http://www.cnn.com/2011/US/02/01/texas.oldest.person.dies/index.html?hpt=T2 reminds me that I've often wondered about th …

For given counting number $n$, consider all permutations $\pi$ of {$1,\ldots,n$}, generate for every $\pi$ its Robinson-Schensted pair of standard tableaux $(P_\pi,Q_\pi)$ and average together all the …

I would like to know if I have discovered or merely rediscovered the following pretty fact. A partition of $[0,1]$ into intervals of lengths $p_{i, i=1\ldots n}$ induces a probability distribution wi …

If you wanted to measure the strength of, say, a chess player, the best way would involve knowing the true value of each position: then you could compute the frequency $W$ with which the player finds …