All Questions
Tagged with mp.mathematical-physics pr.probability
158 questions
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Is there a Gaussian process for the solutions of the wave equation?
Call a Gaussian process $g$ a prior for a topological space $X$ if the realizations of $g$ are (a.s.) contained in $X$ and dense.
Consider the 1D wave equation
$\frac{\partial^2}{\partial t^2}u(t,x)=...
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Formally confirm a formula for a certain three-dimensional constrained integral over the unit cube
The result of the three-dimensional constrained integration (for the Hilbert-Schmidt two-qubit absolute separability probability) over the unit cube $[0,1]^3$
\begin{equation} \label{one}
\int_0^1 \...
- 723
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Convergence of Liouville correlation functions
A key object in Liouville conformal field theory is the random Liouville measure $M$ defined heuristically as $M(d^2x) = :e^{2bX(x)}: d^2x$, where $X$ is a Gaussian free field and $:e^{2bX}:$ denotes ...
user528837
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Additivity of purity of random matrix products
Suppose $M$ is an $n\times n$ matrix with IID random entries drawn from $\mathcal{D}$ and $\sigma$ is the vector of its singular values. Define purity of $M$ as
$$\rho(M)=\frac{n \sum_i \sigma_i^4}{\...
- 2,252
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Random walk in random enviroment
I am looking for a classical analogue of localization for quantum walks.
First, I draw for each point in $x \in \mathbb{Z}^2$ (with some distribution) the numbers $u_x,d_x,l_x,r_x$ such that $u_x+d_x+...
- 1,054
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Probability of close approach for multivariate normal variables
The following problem comes from a physical model of two groups of particles in three dimensions. I need to know the probability that the two groups of particles approach each other within some ...
- 195
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Sum over a product of binomial coefficients related to a collision problem
I am working on a certain collision problem. The probability of forming $j$ particles upon collision of $m$ and $n$ particles is given by the following equation:
$$R\left(n,m,j\right)=\sum_{k=0}^{n}...
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Brownian particles in a box: the probability that a sphere (of some radius) centered on a particle only contains one particle for a duration of time
Imagine I have a set of $(s_1,...,s_N) \in S$ Brownian particles in a box of sidelength $L$, each with the same coefficient of diffusion $D$. We fix one particle at the center of the box, and draw a ...
