# Tagged Questions

**3**

votes

**1**answer

186 views

### Symmetries of the standard probability space

The standard probability space $(I, \mathcal B, \lambda)$ consists of the interval $I = [0,1]$, its Borel $\sigma$-algebra $\mathcal B := \mathcal B(I)$ and Lebesgue measure $\lambda$. In ...

**12**

votes

**4**answers

980 views

### What results would follow from or imply “randomness” of the primes?

This question on random versions of deterministic problems reminded me that many conditional results in number theory hold if the primes are in some sense random, and it is common knowledge that the ...

**19**

votes

**11**answers

1k views

### Random versions of deterministic problems

What are the examples of situations where "randomizing" a problem (or some part of it) and analyzing it using probabilistic techniques yields some insight into its deterministic version?
An example ...

**8**

votes

**4**answers

2k views

### Brownian motion, martingales, Markov Chains - Rosetta Stone

What are the most
fundamental/useful/interesting ways in
which the concepts of Brownian motion,
martingales and markov chains are
related?
I'm a graduate student doing a crash course in ...

**50**

votes

**12**answers

13k views

### What are the big problems in probability theory?

Most branches of mathematics have big, sexy famous open problems. Number theory has the Riemann hypothesis and the Langlands program, among many others. Geometry had the PoincarĂ© conjecture for a long ...

**5**

votes

**3**answers

253 views

### Medium-Sized Calculations and Organization

This is not a math question as much as a process question. For the first time in my (very short) career, I find myself doing one of those messy calculations, where each 'line' of the calculation can ...

**4**

votes

**2**answers

532 views

### Mathematical means of studying large and complex but finite systems?

I want a list of the sort of mathematics/mathematical tools that are applied to the study of complex and probabilistic systems in order to make quantitative and qualitative observations about their ...

**9**

votes

**12**answers

2k views

### probability in number theory

Hi,
I am hearing that there are some great applications of probability theory (or more general measure theory) to number theory. Could anyone recommend some good book(s) on that (or other types of ...