Skip to main content
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
Results tagged with
Search options not deleted user 16702

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_ …
Matthias Ludewig's user avatar
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 …
Matthias Ludewig's user avatar
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 …
Matthias Ludewig's user avatar
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} …
Matthias Ludewig's user avatar