All Questions
10 questions
0
votes
1
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301
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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)=...
18
votes
0
answers
310
views
Profiles of very high dimensional functions
This question comes from trying to understand the recent success of deep neural nets. Neural networks just (crudely speaking) create a very complicated function of very many variables, and then ...
- 96.4k
2
votes
0
answers
192
views
Diffusion equation on mixing of diffusing particles
I am trying to study mixing of diffusing particles like it was done by E. Ben-Naim On the Mixing of Diffusing Particles.
The picture below shows the idea how permutations and inversion numbers reflect ...
6
votes
0
answers
398
views
semiclassical proof of Wigner semicircle
In Terence Tao's discussion of the Gaussian Unitary Ensemble, he derives the Dyson and Airy kernels. The GUE is the probability distribution of the eigenvalues of a random Hermitian matrix.
\[ \int ...
- 22.8k
6
votes
0
answers
411
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Birth-Death Process associated with Orthogonal Polynomials
I have read in various places the following objects are related:
orthogonal polynomials
birth-death processes
Lattice paths
continued fractions
After a lot of searching online, I found sketches ...
- 22.8k
3
votes
0
answers
188
views
Does the existence of an asymtpotic density imply the existence of a measure on infinite dimensional (path) space?
This question is related to the following question
Question about a Limit of Gaussian Integrals and how it relates to Path Integration (if at all)?
A couple of authors have observed that composing a ...
- 265
11
votes
1
answer
1k
views
Question about a Limit of Gaussian Integrals and how it relates to Path Integration (if at all)?
I have come across a limit of Gaussian integrals in the literature and am wondering if this is a well known result.
The background for this problem comes from the composition of Brownian motion and ...
- 265
5
votes
1
answer
623
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For which values of $N$ is known the Lieb-Simon Inequality for $Z_N$ Models ?
Background:
Let $\mathbb Z^d$ denote the $d$-dimensional integer lattice with norm $|x|=\sum_i|x_i|$.
For each $x\in\mathbb Z^d$ we associate a spin variable, $\sigma_x$ taking values on the set
$\{...
- 2,044
6
votes
2
answers
5k
views
Can I relate the L1 norm of a function to its Fourier expansion?
I would like to express the integral of the absolute value of a real-valued function $f$ (over a finite interval) in terms of the Fourier coefficients of $f$. Failing that, I would like to know of any ...
- 185
6
votes
3
answers
423
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Infinite electrical networks and possible connections with LERW
I've been exposed to various problems involving infinite circuits but never seen an extensive treatment on the subject. The main problem I am referring to is
Given a lattice L, we turn it into a ...
- 85.6k