# Tagged Questions

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### Distribution of entries of a doubly-sorted random matrix

Take an $n \times n$ random matrix whose entries are i.i.d. with uniform distribution in $[0,1]$. Look at the sums of the elements of each row and then permute the rows so that these sums form an ...
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### Azuma's Inequality when the conditions hold with high probability?

In Azuma's Inequality, is the statement true when $|X_k - X_{k-1}| < c_k$ almost surely rather than with probability 1? If not, is there another result which gives strong concentration when the ...
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### The degrees in a random subgraph

Fix some positive integers $N$ and $d_k$, $k=1,2,\dots$ with $N=\sum_{k=1}^\infty d_k$. Suppose you have a graph $G$ taken randomly uniformly among the set of all (unoriented) graphs with $N$ ...
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### A Variance-Tail Description for Continuous Probability Distributions

Start with a continuous probability distribution given by a density function f(x). Let X be a real random variable whose distribution is given by the probability distribution. I would like to ask ...
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### Is the maximum tree-path length distributed lognormally (in the limit) ?

Consider a full binary tree with $k>10$ levels. Let the lengths of individual edges in this tree be i.i.d. random variables with finite moments. Then total lengths of the $2^{k-1}$ source-to-sink ...
Randomly select $n$ numbers from the universe $\{1,2\dots,m\}$ without replacement, and sort the numbers in ascending order. We can get a list of number $\{(a_1,a_2,\dots,a_n\)}$, and then we can ...
Maple seems to suggest that for any real $a\ge 1$ and positive integer $K$ and $n$ with $K\le n/(a+1)$ one has  a^n + na^{n-1} + \binom{n}{2}a^{n-2} +...+ \binom{n}{K}a^{n-K} \le a^{n-K} ...