# Tagged Questions

**11**

votes

**1**answer

304 views

### Longest of random worm-like paths in $\mathbb{Z}^2$

Imagine at each lattice point of $\mathbb{Z}^2$ within $[1,3n]^2$,
with coordinates
$\equiv 2 \mod 3$,
we place, with equal probability, one of these six patterns:
The result ...

**1**

vote

**1**answer

165 views

### A square-squareroot integer race sequence involving primes

I wonder what is the expected behavior of this process?
Let
$f^2_{\mathrm{next}}(n) =$ the next prime after $n^2$.
$g_{\mathrm{sqrt}}(n) = \lfloor \sqrt{n} \rfloor$.
Now iterate as ...

**9**

votes

**0**answers

207 views

### Generating random finite groups

I would like a method to efficiently generate a random finite group of a given order $n$.
If there are $g(n)$ non-isomorphic groups of order $n$,
ideally each group would occur with probability ...

**0**

votes

**1**answer

200 views

### Probability generating function zero implies random variable is infinite

Let $V$ be a random variable supported on the nonnegative integers (including $\infty$) and $f(x) = \mathbf E x^V$ be the probability generating function. In our model $V$ is the number of visits to ...

**3**

votes

**2**answers

227 views

### Cardinality of intersection of a random subset with a fixed subset

How can I simply prove the following fact:
Let $A := \{1, \dots n \}$ and $B := \{1, \dots, \lfloor \frac{n}{4} \rfloor \}$. Let $d \in (0,1)$ and let $R$ be a randomly choosen (with uniform ...

**13**

votes

**1**answer

437 views

### Does erosion mix faster than a riffle shuffle?

It is a famous result of Aldous and Diaconis1 that
seven shuffles are necessary and suffice to approximately
randomize 52 cards.2
Here the shuffles are the standard riffle shuffle, where the ...

**6**

votes

**1**answer

508 views

### Calculating a specific joint probability involving sums of binomial distributions

The following might look like a simple problem - but the question has been unanswered for more than a week on math.stackexchange.com, and I have asked quite a few of the Ph.d. students at our ...

**5**

votes

**1**answer

596 views

### Bounding the entropy of a convolution

Say we have a function $f:\mathbb{Z}_2^n \to \mathbb{R}$, such that $\sum _{x\in \mathbb{Z}_2^n} f(x)^2 = 1$ (so we can think of $\{ f(x)^2\} _{x\in \mathbb{Z}_2^n}$ as a distribution). It is natural ...

**3**

votes

**2**answers

206 views

### Designing a tree to match a distribution

I want to design a tree to approximate a given
sequence of numbers, in the following sense.
Let $X=(x_1,\ldots,x_n)$ be $n$ numbers, with $0 < x_i \le 1$
and $\sum_i x_1 = 1$.
For a rooted tree ...

**1**

vote

**2**answers

473 views

### Randomized algorithm?

The problem is as follows. Given a set $S$ of natural numbers of size $n$ where each $x_i \in S$ is from the set $[n^2]$. Elements of $S$ are not necessarily pairwise different, i.e., there can be ...

**2**

votes

**4**answers

434 views

### Statistical computation in matrix. Rows before columns? riddle..

First I'll phrase the question as a riddle, and than as a general math problem.
We have 12 lettered vases $(A,B,...,L)$, in each vase there are 30 numbered balls (1-30). In each ball there is some ...

**1**

vote

**1**answer

4k views

### How to compute KL-divergence when PMF contains 0s?

From the Wikipedia page on Kullback-Leibler divergence, the way to compute this metric is to utilize the following formula:
The way I understand this is to compute the PMFs of two given sample sets ...