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Results tagged with stochastic-processes
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user 68927
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
3
votes
1
answer
451
views
Orthonormal frame bundles on a manifold
Let $(\mathcal{M},g)$ be a torsion free compact Riemannian manifold of dimension $n$. Hence from the metric we know there is an associated horizontal sub-bundle $H_u F \mathcal{M}$ of the orthonormal …
- 396
7
votes
1
answer
728
views
Feynman-Kac formula for the GFF
The Feynman-Kac formula says that $$ \exp(-t(-\Delta+V(X)))(x,y) = \mathbb{E}_{\gamma(0)=x,\gamma(t)=y}\left[\exp(-\int_0^t V\circ\gamma)\right] $$ where $\Delta$ is the Laplacian on $L^2(\mathbb{R}^n …
- 396
13
votes
1
answer
1k
views
Mathematical construction of $\phi^4$ Euclidean field theory
One possible approach to constructive field theory is to define it on a lattice and take the scaling limit, and there are famous results stating that in $d\geq4$ this cannot lead to a non-trivial theo …
- 396