Questions tagged [random]

Question 1

I plot the Gaussian distribution based on the mathematical definition and using the np.random.normal generator: Next, using different interval steps and other parameters, I subtracted both twice to ...

Question 2

In the book by Da Prato on SPDEs the following is claimed: suppose W is a Q-Wiener process with values in $L^2(\mathbb{R}^d)$. Thus, by the very definition, $W_t(\cdot)$ is a random variable with ...

Question 3

Assumme a variable $x$ is positively correlated with an event $A$, by which I mean that $\rho_{x,1_{A}} > 0$, where $\rho$ is the correlation coefficient and $1_{A}$ is the indicator function of ...

Question 4

What is the most efficient known algorithm for generating random $n \times n$ invertible matrices with coefficients in the finite field $\mathbb{F}_p$? Of course, I mean sampling from the uniform ...

Question 5

What zeros of a function were once believed to be pseudorandomly distributed but turned out to follow patterns ? I do not consider the GRH or ERH to be valid examples since they are conjectured to be ...

Question 6

I am writing a c++ library for very large integers. (very large meaning hundreds of digits or more). I want to add a function $Y = \operatorname{randBig}(X)$ to generate a very large, uniformly ...

Question 7

We can take two primes $p_1$ and $p_2$ and consider the smallest non-negative integers $x_1$ and $x_2$ that are equivalent to $x_1 \equiv \left(1 \bmod p_1 \right) \land \left(0 \bmod p_2 \right)$ $...

Question 8

Consider a reversible markov chain with transition matrix $P$, and eigenvalues $1 = \lambda_1 \geq\lambda_2\dots\geq \lambda_n\geq-1$. Now, the mixing time depends on the eigenvalues with the largest ...

Question 9

Given a random variable $X$ on $(\Omega,\mathcal{F},\mathbb{P})$ and an event $E$, what is the intuition behind the trace $\sigma$-algebra $\sigma(X)\cap E=\{A\cap E:A\in\sigma(X)\}$? What is it used ...

Question 10

For the most part I understand the mathematical statement of Szemerédi's Regularity Lemma: it states that any large graph's vertices can be partitioned into k parts (groups) of equal or nearly equal ...

Question 11

I recall seeing an algorithm in Knuth that builds on two unrelated random number generators to make a better one. Use generator 1 to populate a table. Use generator 2 to generate an index and select ...

Question 12

Consider the random number generators: \begin{equation*} (i) ~ y_{i+1} = 5y_i + 3 \mod 2^5, \qquad (ii) ~ x_{i+1} = 3x_i \mod 31 \end{equation*} The generators $(i), (ii)$ have periods $32, 30$ ...

Question 13

In the Monobit Test for randomness, the threshold for passing or failing is based on a confidence interval. I understand that a 1% significance level (99% confidence) results in a larger threshold ...

Question 14

Is there a math procedure that will theoretically generate a point on the Sierpinski Triangle uniformly at random? There are a bunch of numerical approximate methods I can think of (e.g. just ...

Question 15

It came up recently in a coding task I was doing that I needed to choose a 'random line' inside of the unit circle. My first thought was to choose two points inside the unit circle at random (i.e. by ...

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Questions tagged [random]

analysis of the difference in the description of statistical distributions obtained mathematically/physically/computer-generated?

Joint measurability Q-Wiener process in L^2

Looking for a crisp argument about the correlation with a complementary event

Generating random samples from $\operatorname{GL}_n(\mathbb{F}_p)$

What zeros of a function were once believed to be pseudorandomly distributed but turned out to follow patterns? [closed]

Generating uniformly distributed large integer on a given range from smaller random integers

Chinese remainder theorem and randomness related to "unit vectors"

Lazy markov chains mix faster

Intuition regarding trace $\sigma$-algebras and its uses

Understanding the regularization lemma and what can be said about graphs representing the real word by applying this lemma?

Trying to recall name of algorithm that generates a "good" random sequence from two poorer ones

Period of combination of mixed random number generator

How is the threshold determined in the Monobit Test, and why is it larger for a 1% significance level than for 5%?

Generating a uniformly random point on the Sierpinski Triangle?

How to choose a ''uniformly random'' line inside a circle.

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