Search Results
Search type | Search syntax |
---|---|
Tags | [tag] |
Exact | "words here" |
Author |
user:1234 user:me (yours) |
Score |
score:3 (3+) score:0 (none) |
Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
Views | views:250 |
Code | code:"if (foo != bar)" |
Sections |
title:apples body:"apples oranges" |
URL | url:"*.example.com" |
Saves | in:saves |
Status |
closed:yes duplicate:no migrated:no wiki:no |
Types |
is:question is:answer |
Exclude |
-[tag] -apples |
For more details on advanced search visit our help page |
The Laplacian matrix is the representation of a graph in matrix form.
4
votes
Accepted
heat kernel on closed manifolds - error in Chavel's book?
Yes, there is indeed a mistake. Chavels Lemma 2 on page 153 tells you that
$$L(H_k * F) = (LH_k)*F - F,$$
so if you define $F = \sum_{l=1}^\infty (LH_k)^{*l}$ and $p= H_k + H_k * F$, then
$$ L p = LH_ …
5
votes
Accepted
Stochastic interpretation of heat kernel on fiber bundle
Let $P\longrightarrow M$ be a $G$ principal bundle endowed with a connection $1$-form $\omega$ (which has values in the Lie algebra $\mathfrak{g}$). If $X_t^x$ denotes Brownian motion on $M$ starting …
3
votes
The complex heat kernel on a Riemann manifold
As far as I know, the term "Mehler Kernel" is used for the integral kernel of the heat equation corresponding the the harmonic oscillator,
$$ \partial_tu + \Delta u + x^2 u = 0.$$
The equation you are …
5
votes
2
answers
664
views
Closed formula for heat kernel
Is there, similar to the Mehler kernel, a closed formula for the heat kernel of the heat equation associated to the Laplacian
$$ -\sum_j \frac{d^2}{dx_j^2} + 2\sqrt{-1} \sum_j \lambda_j \frac{d}{dx_j} …