# Tagged Questions

**0**

votes

**1**answer

128 views

### How to calculate eigenvalue density function of $XX^\dagger$ from the density function of X

Let X be a complex random matrix, which has the probability function (drawn from the ensemble) V($XX^\dagger$), where V(x) is some function which guaranties good behavior at infinity. Note the unitary ...

**1**

vote

**0**answers

332 views

### Prove that the sum of a certain infinite series is 1

Prove the (numerically-evident) proposition that
\begin{equation}
\Sigma_{i=0}^\infty f(i) = 1,
\end{equation}
where
\begin{equation}
f(i)= 2^{-4 i-6} q(i) \frac{\Gamma(3 i+\frac{5}{2}) \Gamma(5 ...

**3**

votes

**2**answers

286 views

### Probability distribution for two-state system that depends on residence time

I am a statistical physicist, and I've come across a problem that I don't know how to solve. I believe my issue lies with how to formulate it mathematically. I'd be very grateful for any assistance, ...

**3**

votes

**1**answer

185 views

### Exact sampling from 2D Ising model where coupling is constant?

What progress has been made towards sampling from the 2D lattice Ising model with the following Hamiltonian:
$H=-J\sum_{\langle i,j \rangle}S_iS_j - \sum_i b_iS_i$
Where the first sum runs over all ...

**2**

votes

**0**answers

181 views

### Is connected correlation/cumulant expansion additive?

Say X is a free field or a Gaussian random variable.
Then I want to analyse the connected correlation, $<(X + a (X^2 - \langle X^2 \rangle))^n>_c$
I think that for $n \geq 4$ there are no ...

**8**

votes

**1**answer

625 views

### What is quantum Brownian motion?

It seems that the current state of quantum Brownian motion is ill-defined. The best survey I can find is this one by László Erdös, but the closest the quantum Brownian motion comes to appearing is in ...

**5**

votes

**0**answers

152 views

### Given that a conditional measure is Gaussian, how bad can the original measure be?

Let $X$ and $Y$ be Banach spaces, and let $\varphi : X \to Y$ be a continuous linear map. Suppose that $\mathbb P$ is a probability measure on $X$ which satisfies the continuous disintegration ...

**6**

votes

**2**answers

409 views

### When is a space of measures a measurable space?

Let $X$ denote a measurable space, that is, a set equipped with a $\sigma$-algebra $\Sigma(X)$. Let $M(X)$ denote the space of real-valued measures over $X$. This is a vector space over the real ...

**2**

votes

**2**answers

696 views

### Singular Value Decomposition of Noisy Matrices

I am an engineer who makes measurements of a variable over a grid
of, say, $m\times n$. Since these are actual measurements, the true
values are always corrupted by noise, and what I measure is a ...

**0**

votes

**0**answers

387 views

### Find closed form for comparison of two binomial random variable: solve inequality

Hi, Dear All,
I come up with this problem, which I think for a long time without a good answer.
Suppose two independent random variables $X \sim \mathrm{Binomial}(n, p)$ and $Y \sim ...

**1**

vote

**1**answer

252 views

### Stieltjes convolution with white noise

I'm looking for a reference that would discuss a Stieltjes convolution between a wiener process and a function of bounded variation. Additionally, I had a question about this sort of convolution.
Is ...

**10**

votes

**7**answers

978 views

### Probabilistic (and other mathematical) methods of physics without the physics?

Many of the methods of physics are vastly more general than their use in that discipline. For example, information theory overlaps with a lot of statistical mechanics, and the latter actually ...

**0**

votes

**1**answer

850 views

### Can you interpret this divergent integral?

In this ArXiv paper by Wilk and Wlodarczyk (published in Physical Review Letters), equation 16 has essentially the following definition of a function:
$$\text{f(x)=}\frac{c}{2Dx^2}\exp[\int^x_0 ...

**1**

vote

**0**answers

252 views

### Differential operator with image of its Frechet derivative in the nullspace of operator adjoint?

Is there an example of a differential operator $A(z)$ with parameter $z \in \mathbb{R}^d$ and Frechet derivative $A_z(z)$ such that $\mathrm{im}(A_z(z)) \subseteq \mathrm{ker}(A^T(z))$. Can this still ...

**7**

votes

**3**answers

1k views

### randomness in nature [closed]

What is the explanation of the apparent randomness of high-level phenomena in nature?
For example the distribution of females vs. males in a population (I am referring to randomness in terms of the ...

**3**

votes

**2**answers

420 views

### Monte Carlo simulations

I was wondering what were the models of statistical physics that are still considered difficult/slow to simulate (exactly, or approximately) with the current technology of Monte Carlo approaches. I ...