# What is Kolmogorov: Definition and 18 Discussions

Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров, IPA: [ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf] (listen), 25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.

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1. ### I Bell vs Kolmogorov: Unravelling Probability Theory Limits

For some reason on this forums here I found some weird opinions that Bell's inequality were somehow disqualifying classical probability theory in general rather then showing merely the limits of locality. I do no understand where that misunderstanding comes from, so I decided to find out. Let's...
2. ### I Quantum physics vs Probability theory

Because I do have a background in the latter it was originally very difficult for me to understand some aspects of QP (quantum physics) when I initially learned it. More specifically whenever probabilities were involved I couldn’t really make full sense of it while I never had any problems...
3. ### A Understanding Kolmogorov-Smirnov Test Results for Random Number Generators

Hi all, I have some doubts regarding the Kolmogorov test: I made a simple c++ program generating two samples of random numbers following a Landau distribution (I used the "hit and miss" method). I made the Kolmogorov test, in order to check the randomness of the generator, but I'm having some...
4. ### Structure function in turbulence

Hey guys, I need your help. I have to write a homework and we are actually looking at structure functions (Kolmogorov 41 and so on), but I have no clue what it does. So I have formulas, but I do not understand what a structure function is. Is it something in the "real world" or is it just a way...
5. ### I What "language" means in Kolmogorov complexity?

Please help me to understand the answer I found on mathoverflow. The question was: "Do all uncountable sets contain elements with infinite Kolmogorov complexity?" The reasoning is clear for me, but I'd like to understand every word of the answer, which is the following: "...given a language...
6. ### Kolmogorov Entropy: Intuitive Understanding & Relation to Shannon Entropy

Dear all, I'm trying to have an intuition of what Kolmogorov Entropy for a dynamical system means. In particular, 1. what is Kolmogorov Entropy trying to quantify? (what are the units of KS Entropy, is it bits or bits/seconds). 2. What is the relation of KS entropy to Shannon Entropy? 3. In...
7. ### Chapman Kolmogorov Th. - generality?

Does the Chapman - Kolmogorov equation hold for an arbitrary stochastic process? The current wikipedia article on "Stochastic process" ( https://en.wikipedia.org/wiki/Stochastic_process ) seems to say that the Chapman-Kolmogorov equation is not valid for an arbitrary stochastic process. I...
8. ### Help with Kolmogorov Complexity proof

Hey, has anyone here done Kolmogorov complexity? I hadn't, and I was just reading the Wikipedia page to start learning it. The core concept makes sense: The Kolmogorov complexity for a a string s, K(s) is equivalent to the length of a program that generates that string (It can be any math...
9. ### Can the Kolmogorov definition of the conditional probability be proven

It seems weird that such a relatively complex concept is simply given as a definition in most textbooks and then dismissed for further explanation other than using it intact or as a basis for further proofs.
10. ### Steady State Solution of Forward Kolmogorov Equation

Essentially, this looks like a differential equation problem but being rusty on differential equations I am a little stuck. Homework Statement Consider the following SDE d\sigma = a(\sigma,t)dt + b(\sigma,t)dW The Forward Equation (FKE) is given by \frac{\partial p}{\partial t} =...
11. ### Kolmogorov smirnov in r - cannot compute correct p-values with ties

Hi, I'm trying to use the kolmogorov smirnov test in in R to compare one distribution with another. I'm getting the following error: cannot compute correct p-values with ties I think this is because the dataset that I am using has in the first instance around 2000 values, and the second...
12. ### K41 Kolmogorov scaling relation and structure functions (turbulence)

Hi there. I am having trouble interpreting the Kolmogorov K41 scaling relation for homogeneous and isotropic turbulence: S_{p}(l) = <\delta u(l)^{p}> = <|u(r+l) - u(r)|^{p}> \propto (\epsilon l)^{p/3} where l is the length of displacement between two points under consideration in the...
13. ### Kolmogorov & Fomin's Elements of Theory: Real Analysis or Lebesque?

I'm looking for a Real Analysis book to start with, besides Spivak. On Amazon, one of the reviewers said it was good as a subsequent book for learning Functional Analysis/Lebesque Integration, while another said it was a good introduction to Real Analysis. For those of you that have read it...
14. ### Solution of the Kolmogorov forward equation for a linear process

Consider the 1-D linear system governed by: "dx/dt = a*x(t) + n(t)" where "a" is a scalar and: x(t) = system state n(t) ~ N(0, sigma^2) **************************** We can write Ito's stochastic differential equation of the previous process as: "dx = a*x*dt + 1/2*sigma^2*dW_t"...
15. ### Definition of a Kolmogorov Space

Homework Statement Can a T_{0} topological space be created from the indiscrete topology of a set with only one element?
16. ### What are the differences between Blum and Kolmogorov complexities?

Are they equivalent in some sense?
17. ### Kolmogorov complexity of SAT

I'm not entirely clear on the concept of kolmogorov complexity. Does it mean that the a certain string is complex if there is no combinatorial (not sequential) circuit which outputs that string or does it mean that a certain string is complex if there is no program which can output that string...
18. ### Are Strings Kolmogorov-Random Actually Random?

Are strings that are Kolmogorov-random actually random in the usual sense? An incompressible string probably won't contain this post anywhere in it, but a random one can.