# Tagged Questions

**4**

votes

**1**answer

141 views

### what characterizes a characteristic function of a probability measure in separable Hilbert spaces?

As we all know on real line $\mathbb{R}$, the following is valid
A $\mathbb{C}$-valued function $\varphi$ is a characteristic function of a probability measure on $\mathbb{R}$ if and only if ...

**2**

votes

**2**answers

195 views

### Intuition on Lindeberg condition

I want to know how Lindeberg came up with the condition which is sufficient for CLT to hold ? What is the intuition behind such an expression ?

**13**

votes

**1**answer

897 views

### Intuition of law of iterated logarithm?

Let $X_i$ be iid random variables with $EX_i = 0$ and $Var X_i=1$ and $S_n=X_1+\cdots+X_n$. Then the law of the iterated logarithm says almost everywhere we have
...

**8**

votes

**2**answers

703 views

### Intuition behind the spectral density of random matrices

Hi,
I have read that the spectral density of an NxN random matrix consisting of iid random variables with zero mean and unit variance converges as N goes to infinity to the uniform distribution on ...

**8**

votes

**0**answers

384 views

### High-dimensional geometry: Top-down Vs. Bottom-up

There are several ways to leverage one's intuition from low-dimensional geometry to understand high-dimensional phenomena. For example, one can get a clearer picture of the behaviour of ...

**1**

vote

**0**answers

297 views

### Relationship between R-transform and free convolution of random matrices?

I've been using the R-transform to calculate the free convolution of the eigenvalue spectra of two random matrices and I am trying to understand how it works, and in particular how it relates to ...

**13**

votes

**0**answers

307 views

### Why, and how badly, does the proof of “no percolation at the critical point in half-spaces” fail for full spaces?

The proof by Barsky et. al. that there is no percolation in half-spaces proceeds by a dynamic renormalization argument. The proof couples critical percolation in the half-space $\mathbb{H}^d$ with a ...

**5**

votes

**1**answer

588 views

### Intuitive “proof” or explanation of a result in Friedman's urn

Let $g, r, a, b$ be positive integers. In Friedman's urn model we have an urn with $r$ red and $g$ green balls in it. In each step we take one ball out of urn, register its color and return it to the ...

**4**

votes

**1**answer

2k views

### Skellam distribution: Deep connection between Poisson distributions and Bessel function?

The probability mass function for the Skellam distribution for a count difference $k=n_1-n_2$ from two Poisson-distributed variables with means $\mu_1$ and $\mu_2$ is given by:
$$
f(k;\mu_1,\mu_2)= ...

**51**

votes

**9**answers

7k views

### How is it that you can guess if one of a pair of random numbers is larger with probability > 1/2?

My apologies if this is too elementary, but it's been years since I heard of this paradox and I've never heard a satisfactory explanation. I've already tried it on my fair share of math Ph.D.'s, and ...

**79**

votes

**25**answers

22k views

### What is convolution intuitively?

If random variable $X$ has a probability distribution of $f(x)$ and random variable $Y$ has a probability distribution $g(x)$ then $(f*g)(x)$, the convolution of $f$ and $g$, is the probability ...